Exhibit 5.1

Skadden, Arps, Slate, Meagher & Flom LLP

Four Times Square

New York, New York 10036

November 4, 2010

American Capital Agency Corp.

2 Bethesda Metro Center, 14th Floor

Bethesda, Maryland 20814

Re: American Capital Agency Corp. Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special counsel to American Capital Agency Corp., a Delaware corporation (the “Company”), in connection with the automatic shelf registration statement on Form S-3 to be filed on the date hereof by the Company (the “Registration Statement”) with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933 (the “Act”). The Registration Statement relates to, among other things, the issuance and sale by the Company, from time to time pursuant to Rule 415 of the General Rules and Regulations promulgated under the Act, of the following securities of the Company: (i) an indeterminate number of shares of common stock of the Company, par value $.01 per share (the “Common Stock”), (ii) an indeterminate number of shares of preferred stock of the Company in one or more series, par value $.01 per share (the “Preferred Stock”), and (iii) such indeterminate number of shares of Common Stock or Preferred Stock as may be issued upon conversion of any Preferred Stock (collectively, the “Indeterminate Securities”). The Common Stock, the Preferred Stock and the Indeterminate Securities are collectively referred herein as the “Offered Securities”.

This opinion is being delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) the Registration Statement, (ii) the Amended and Restated Certificate of Incorporation of the Company, as certified by the Secretary of State of the State of Delaware (the “Certificate of Incorporation”), (iii) the Amended and Restated By-laws of the Company, as currently in effect (the “By-Laws”), (iv) certain resolutions of the board of

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directors of the Company (the “Board”) relating to the registration of the Offered Securities and (v) a specimen certificate representing the Common Stock.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company, and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents, certificates and records as we have deemed necessary or appropriate as a basis for the opinions set forth herein.

In our examination, we have assumed the legal capacity of all natural persons, the genuineness of all signatures, including endorsements, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified, conformed or photostatic copies and the authenticity of the originals of such copies. In making our examination of documents executed or to be executed, we have assumed that the parties thereto, other than the Company, had or will have the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents, and the validity and binding effect thereof on such parties. In addition, we have assumed that the terms of the Offered Securities and the issuance and sale thereof will have been established so as not to, and the Company’s compliance therewith will not, violate, conflict with or constitute a default under (i) the Certificate of Incorporation or By-Laws, (ii) any agreement or instrument to which the Company is subject, (iii) any law, rule or regulation to which the Company is subject, (iv) any judicial or regulatory order or decree of any governmental authority or (v) any consent, approval, license, authorization or validation of, or filing, recording or registration with, any governmental authority. As to any facts material to the opinions expressed herein which we have not independently established or verified, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others.

Our opinions set forth herein are limited to the provisions of the Delaware General Corporation Law (the “DGCL”) that, in our experience, are normally applicable to transactions of the type contemplated by the Registration Statement and, to the extent that judicial or regulatory orders or decrees or consents, approvals, licenses, authorizations, validations, filings, recordings or registrations with governmental authorities are relevant, to those required under such laws (all of the foregoing being referred to as “Opined on Law”). We do not express any opinion with respect to the laws of any jurisdiction other than Opined on Law or as to the effect of any such non-Opined on Law on the opinions herein stated. The Offered Securities may be issued from time to time on a delayed or continuous basis, and this opinion is limited to the laws, including the rules and regulations under the Act, as in effect on the date hereof, which laws are subject to change with possible retroactive effect.

Based upon and subject to the foregoing and to the limitations, qualifications, exceptions and assumptions set forth herein, we are of the opinion that:

1.    With respect to any shares of Common Stock to be offered by the Company, including any Indeterminate Securities, pursuant to the Registration Statement (the

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“Offered Common Shares”), when (i) the Registration Statement has become effective under the Act, (ii) an appropriate prospectus supplement or free writing prospectus with respect to the Offered Common Shares has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (iii) if the Offered Common Shares are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Common Shares, including with respect to any Indeterminate Securities issuable in respect of conversion rights of Preferred Stock registered pursuant to the Registration Statement, has been duly authorized, executed and delivered by the Company and the other parties thereto, (iv) the Board, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance and sale of the Offered Common Shares, the consideration to be received therefor and related matters, (v) if the issuance of the Offered Common Shares is certificated, certificates approved by the Board and in the form required by the DGCL and the By-Laws representing the Offered Common Shares are duly executed and countersigned, and (vi) the Offered Common Shares are registered in the Company’s share registry and delivered upon payment of the agreed upon consideration therefor, the Offered Common Shares (including any Offered Common Shares duly issued upon conversion of any Preferred Stock), when issued and sold or otherwise distributed in accordance with any applicable underwriting agreement with respect to the Offered Common Shares or any other duly authorized, executed and delivered valid and binding purchase or agency agreement, will be duly authorized, validly issued, fully paid and non-assessable, provided that the consideration therefor is not less than the par value thereof.

2.    With respect to the shares of any series of Preferred Stock to be offered by the Company, including any Indeterminate Securities, pursuant to the Registration Statement (the “Offered Preferred Shares”), when (i) the Registration Statement has become effective under the Act, (ii) an appropriate prospectus supplement or free writing prospectus with respect to the Offered Preferred Shares has been prepared, delivered and filed in compliance with the Act and the applicable rules and regulations thereunder, (iii) if the Offered Preferred Shares are to be sold pursuant to a firm commitment underwritten offering, the underwriting agreement with respect to the Offered Preferred Shares, including with respect to any Indeterminate Securities issuable in respect of conversion rights of such Offered Preferred Shares, has been duly authorized, executed and delivered by the Company and the other parties thereto, (iv) the Board, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary corporate action to approve the issuance, sale and terms of the Offered Preferred Shares, the consideration to be received therefor and related matters, including the adoption of a Certificate of Designation for the Offered Preferred Shares and, if applicable, any Indeterminate Securities (each, a “Certificate of Designation”) in accordance with Certificate of Incorporation, By-Laws and the applicable provisions of the DGCL, (v) the filing of any such Certificate of Designation has been filed with the Secretary of State of Delaware, (vi) if the issuance of the Offered Preferred Shares is certificated, certificates approved by the Board in the form required by the DGCL, the applicable Certificate of Designation and the By-Laws representing the Offered Preferred Shares are duly executed and countersigned, and (vii) the Offered Preferred Shares are registered in the Company’s share registry and delivered upon payment of the agreed upon consideration therefor, the Offered Preferred Shares (including any Offered Preferred Shares duly issued upon conversion of any Preferred Stock),

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when issued and sold or otherwise distributed in accordance with any applicable underwriting agreement with respect to the Offered Preferred Shares or any other duly authorized, executed and delivered valid and binding purchase or agency agreement, will be duly authorized, validly issued, fully paid and non-assessable, provided that the consideration therefor is not less than the par value thereof.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also hereby consent to the use of our name under the heading “Legal Matters” in the prospectus which forms a part of the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission promulgated thereunder. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

Very truly yours,

/s/  Skadden, Arps, Slate, Meagher & Flom LLP