Exhibit 99.1

CORTEX PHARMACEUTICALS

INVESTOR UPDATE

CONFERENCE CALL

10/26/2006

4:00PM

Operator: Greetings, ladies and gentlemen, and welcome to the Cortex Pharmaceuticals, Inc. Investor Update Conference call. At this time, all participants are in a listen-only mode. A brief question-and-answer session will follow the formal presentation. If anyone should require operator assistance during the conference, please press *0 on your telephone keypad. As a reminder, this conference is being recorded.

This conference call contains forward-looking statements concerning Cortex’s business, research and development activities. Such activities are subject to a number of risk factors, including the risks that Cortex’s products may be unsafe or ineffective for any or all of the proposed indications and that preclinical and clinical studies may at any point be suspended or take substantially longer than anticipated to complete.

In addition, competitors may challenge or design around Cortex patents or develop competing technologies. These and other risks are discussed in Cortex’s filings with the Securities and Exchange Commission. Also as discussed in the Company’s Securities and Exchange Commission filings, Cortex’s proposed products will require additional research, lengthy and costly preclinical and clinical testing, and regulatory approval. The AMPAKINE^® compounds are investigational drugs, and have not yet been approved in the treatment of any disease. It is now my pleasure to introduce your host, Dr. Roger Stoll, President and CEO. Thank you Dr. Stoll, you may begin.

Roger G. Stoll, Ph.D.-Cortex Pharmaceuticals-Chairman-President-CEO

Good afternoon everyone. Today I plan to discuss the very intensive effort undertaken by Cortex over the past several months to study the toxicology of CX717, which culminated in the recent decision by the FDA to lift the clinical hold. My comments are more extensive than typically would be the case for a shareholders conference call, but we have a great deal of material to review.

Also, when I conclude my comments, there will be time for question-and-answer from the participants in this conference call. Before I go directly to the discussion and some of our findings and conclusions, I would like to be sure that everyone starts with the same background knowledge related to the clinical hold. I would like to go through a chronology at this point.

1

Cortex was notified on the afternoon of March 31, 2006 that CX717 would be placed on clinical hold. By corresponding with the FDA and involving several consultants, we were able to establish by early May 2006, the information desired by the agency to help them decide whether the clinical hold could be lifted. I again need to emphasize that the clinical hold related to animal toxicology findings and not to any problems associated with human testing. The FDA requested that we obtain the following information and submit a complete response to them at a point in time when all the data could be submitted simultaneously. The information desired was: (a) Evaluate additional segments of tissue from the original 13 week primate toxicology study, to determine the full extent of the histopathological changes noted in the particular target organ of the monkey; (b) Conduct a one week acute toxicology study in monkeys at much higher doses, if possible, and conduct further histopathological assessments; and (c) Conduct a 2 week toxicology study in rats, at much higher doses, if possible. In order to comply with these requests Cortex had to conduct a new series of range finding toxicology studies, using a new US based contract research organization. We successfully reached higher dosing in both species and then initiated the requested studies.

At our shareholders meeting in May 2006, we reviewed the requests made by the FDA and provided the timelines for the completion of the studies requested, and submission of the desired information to the FDA. We had a graph, which showed the end of August for submission of the data to the FDA, and the end of September for obtaining a response from the agency. The actual dates for the mailing of the completed response, turned out to be September 8, 2006 and the verbal response from the agency came on October 6, 2006. Considering we had to have all the work conducted through our outside contract research organizations, we came within one week of meeting the target date set in May 2006, which was a fine job by all of our employees, but particularly by Steve Johnson, our VP of preclinical development, in steering this project to completion. By the way, the FDA also met its timelines in responding to Cortex.

The good news is that the FDA lifted the clinical hold, and allowed Cortex to continue clinical testing of CX717. I should explain that when the FDA called Dr. Mansbach with their decision, it boiled down to a decision that to lift the clinical hold immediately, we had to accept their dose limitations. In consulting with our regulatory counsel in Washington and elsewhere, we were strongly advised that we accept their decisions no matter what the dose, and finalize the decision that the hold had been lifted.

The counsel recommended that once we were off hold, we could take our toxicology data that we are now developing and request a review that could liberalize the dosing in the future. At that point, the dosing decision would only focus on what would be an acceptable dose, and would not be related to the clinical hold issue. If we chose to debate the dose level, we might risk not getting removed from hold, which in the mind of our counsel would be the worst decision we could get. As a side-bar, he noted that we should be conscious of the fact,

2

that if other negative data came into the FDA from other competitors, which could impact their view of the AMPA modulators, even if the chemistry was different it could keep us on hold indefinitely without really understanding the basis for such a hold. Obviously, we accepted the FDA’s proposal, and the clinical hold was formally lifted immediately. We received the formal letter, stating that the clinical hold had been lifted, this past Monday, October 23, 2006.

From the time Cortex received the notice of the clinical hold at the end of March to the present, we have utilized 2 regulatory consultants: Dr. Evan Siegel from Ground Zero Pharmaceuticals Inc. and Frank Sasinowski, an Attorney at Hyman, Phelps and McNamara in Washington, DC. We also used 5 different histopathologists and 2 consulting toxicologists to help us plan studies, evaluate the information gathered and review the submission itself, prior to its filing with the FDA.

We have spent approximately 2.5 million dollars in additional unplanned funds to date. The process of assessing the effects of CX717 has not been simple, and each step of this entire program was vetted by experienced industry personnel and consultants.

Now what did we report to the FDA as a result of the questions that they asked us? I have to start out by saying that the AMPAKINE technology is a new science, and one can expect that there will be unknown issues which arise as one develops such a new therapeutic area. Virtually every development project with truly new therapeutic technologies will run into some serious problems which must be resolved before success can be achieved. The histopathological changes which we observed for CX717 are not an easily understood response, and even the experts are not clear on what the toxic manifestations of these observed changes might mean. The fact that the FDA gave us permission to proceed with further human studies, clearly signals that there is a dose range which they are willing to accept. However, the limitations and dosage at this point, means that we must focus on the Alzheimer’s indications, and will not proceed with further studies in ADHD patients at this time. We will need to provide further toxicological data to the FDA, which shows that an increased safety margin can provide the justifications to enable us to get back to the development in ADHD. We will also need to file an IND with another division, the psychiatric division, to be able to pursue longer-term studies in ADHD. This will require completion of additional toxicology studies, which are being completed as we speak. We should be able to make such a decision by the end of first quarter 2007.

Now we’ll get back to the questions asked by the FDA and our findings related to those questions. First, the review of additional tissue samples from monkeys in the original 13 week toxicology study did not reveal any new or more serious findings what so ever. Secondly, we conducted a 7 day very high dose toxicology study in monkeys, and found absolutely none of the cellular

3

histopathology which we saw in the previous 13 week study, as a result of such acute administration of CX717. At the request of some of our histopathology consultants, we also had changed the method used to sacrifice the monkeys, and for fixation of the tissue samples. There were possibilities that the observed cellular changes in the tissues could be artifactual rather than caused by the drug. We then on our own, initiated an additional 14 day high dose toxicology study in monkeys, because we were concerned that the 7 day dosing period had simply been too short to cause the previously observed cellular changes. The good news was that even these longer 14 day studies did not show any of the cellular changes observed in the previous 3 month toxicology studies. The information from the 14 day study has not been submitted to the FDA, because it has just recently become available. It will be submitted to the FDA at a future date, along with other information currently being obtained by Cortex.

Next we were able to assess the tissues from the 14 day high dose rat toxicology study. In this study, we administered what I would term almost heroic doses. At very high doses of 1g per kilo per day or 1.5 g per kilo per day in rats, we saw a dose proportional response related to the cellular changes seen earlier in the 3 month primate study. This clearly related the effects to CX717.

Additionally, studies to assess recovery from the observed cellular changes after cessation of dosing are still underway as we speak, but the early evaluations show that most, but not all of the histological changes, disappear within 2 weeks of cessation of dosing in rats. We still must wait for the last set of data to be completed before we have a complete picture of the recovery potential.

Additionally, Cortex has several studies currently underway. The main areas of focus are related to: (a) a three month monkey toxicology study, started in early July; (b) a three month rat toxicology study started about 1 week later; and (c) we are initiating an electron microscopic assessment of the histological changes to attempt to better understand the cellular components involved in the observed changes, and confirm the types of cells. Finally, we are conducting further studies to assess the potential role of the various metabolites of CX717 on the histopathology. If the pathology is produced by a metabolite, which is formed only to a limited extent in humans, but more extensively in the 2 animal species, the concern may also be reduced. It is our view that the additional data obtained from these extra studies could provide the basis for liberalizing the dose of CX717, which could then be given to humans again for ADHD.

Looking forward now, we certainly view the release of the clinical hold as a very positive step for CX717 and the clinical development program for this agent. The newly established human dose limits set by the FDA are initially conservative, because of the incomplete understanding of the cause and the consequence of the cellular changes observed with CX717. These doses will allow Cortex to safely pursue clinical work with a reasonable chance of success in the fundamental areas of memory enhancement associated with neurological

4

diseases. Based on doses of CX717, which have demonstrated positive effects in numerous animal cognition models both in our hands and in the hands of independent investigators, we can pursue Alzheimer’s disease, quite comfortably. Typically we have found that the cognitive responses require 1-3 mg per kg dose in animals, whereas the hyperactivity responses have always required doses in the range of 10-20 mg per kg. We in fact, have always targeted the cognitive deficits for AMPAKINE drugs, and with the lifting of this clinical hold, we can pursue the Alzheimer’s disease potential for CX717.

The letter which we received this week from the FDA provides further guidance regarding the additional toxicology studies with CX717 that should result in a better understanding of the toxicity, and can lead to higher doses being allowed by the agency. We have found the FDA response as very constructive. As we complete some of the previously described work, Cortex quickly recognized some of these needs, and initiated studies in rats and monkeys with substantially higher doses and with more extensive investigation of the effected tissue. Because of the proactive approach we have taken, some of the histopathological data from the new 3 month study should be available by the end of December 2006. When the full reports from these studies are available, we plan to file these results with the both the neurological division and the psychiatric division of the FDA, so that the development of ADHD indications can also be continued.

In summary, the worst case for Cortex would be if we cannot improve the safety margins and raise the dose available for testing in humans. It would require us to turn to one of our back-up compounds for ADHD. The up-side of such an event is that we do know what to look for both from a toxicological standpoint and efficacy profile in animal models. Thus we would have roadmap for moving more quickly toward an ADHD indication. I should mention that while we have seen some cellular changes in certain tissues related to toxicological assessment of CX717, similar events have not been noted for either CX516 or Organon 24448. This means that the observation is not a problem with low-impact compounds in general. We are moving rapidly to bring along 2 new back-up compounds which are much more potent than CX717, and we should have at least one of these agents in the clinic next year. Because of their higher potency we would quickly assess their suitability for treatment in ADHD.

In conclusion, we are pleased that we can report that our work has resulted in the lifting of the clinical hold, and that we have considerable work underway to help us develop data, which could provide further safety margin for raising the dose of CX717, which could then be administered for humans for ADHD. With the completion of these comments, I now will open the lines for a brief Q&A session.

5