Exhibit 5.01

June 15, 2000

Ceridian Corporation
3311 East Old Shakopee Road
Minneapolis, MN 55425

Re:      Ceridian Corporation
         Registration Statement on Form S-8

Dear Sir or Madam:

         In my capacity as Associate General Counsel and Deputy Secretary to
Ceridian Corporation, a Delaware corporation (the "Company"), I am acting as
counsel for the Company in connection with the registration by the Company of
350,000 shares of its Common Stock, $0.50 par value (the "Shares"), to be issued
pursuant to the Ceridian Corporation 2000 Director Performance Incentive Plan
("Plan"), pursuant to a Registration Statement on Form S-8 filed with the
Securities and Exchange Commission on June 15, 2000.

         In this connection, I have examined originals or copies, certified or
otherwise identified to my satisfaction, of corporate records of the Company and
such other documents that I have considered necessary as a basis for the
opinions expressed herein. In such examination, I have assumed the genuineness
of all signatures, the authenticity of all documents submitted to me as
originals and the conformity with originals of all documents submitted to me as
copies. As to all questions of fact material to such opinions, I have, when
relevant facts were not independently established by me, relied upon statements
of the Company and its officers and of public officials.

         Based upon the foregoing, I advise you that in my opinion that:

         1.       The Shares have been duly authorized and, when issued ,
delivered and paid for in accordance with terms of the Plan, will be validly
issued, fully paid and nonassessable; and

         2.       The Company has the corporate authority to issue the Shares in
the manner and under the terms set forth in the Registration Statement on Form
S-8.

         I hereby consent to the filing of this opinion as Exhibit 5.01 to the
Registration Statement and to its use as part of the Registration Statement.

                                  Very truly yours,

                                  /s/ William E. McDonald
                                  William E. McDonald
                                  Associate General Counsel and Deputy Secretary