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                                  EXHIBIT 99.1

                              [UGLY DUCKLING LOGO]

CONTACTS:   Steven T. Darak
            Senior Vice President & Chief Financial Officer
            (602) 852-6600

            Eugene Heller/Philip Bourdillon
            Silverman Heller Associates
            (310) 208-2550

FOR IMMEDIATE RELEASE

                       UGLY DUCKLING CORPORATION ANNOUNCES
                    COMPLETION OF SUPPLEMENTAL EXCHANGE OFFER

         PHOENIX, Arizona (December 23, 1998) - Ugly Duckling Corporation
(Nasdaq NM: UGLY) announced today the completion of its supplemental exchange
offer, which expired yesterday as scheduled. At the close of business on the
expiration date, the exchange agent reported that a total of 225,425 shares
of common stock were tendered to the Company. The final total of tendered shares
is subject to certain guaranteed delivery procedures and Ugly Duckling's review
and acceptance of all such shares validly tendered. The Company plans to deliver
debentures in exchange for shares in accordance with the exchange offer as soon
as practicable after the expiration of the guaranteed delivery period.

         The exchange offer enabled stockholders to exchange up to 2,536,397 of
shares in the Company for 12%, five-year subordinated debentures. Under the
terms of the offer, each share of common stock was exchangeable for $6.50
principal amount of debentures.

         Stockholders who have questions about the exchange offer may contact
Corporate Investor Communications, Inc., the designated information agent, at
1-888-673-4478 (toll-free).

         Headquartered in Phoenix, Arizona, Ugly Duckling Corporation is a used
car sales and finance company that operates the nation's largest chain of used
car dealerships focused exclusively on the sub-prime market. The Company
underwrites, finances and services sub-prime contracts generated at its 50 plus
Ugly Duckling dealerships. Cygnet Financial Corporation, a wholly owned
subsidiary of the Company, provides various financial services primarily to the
sub-prime segment of the automobile financing industry.

                                     * * *

         This press release may include statements that constitute
forward-looking statements, usually containing the words "believe," "estimate,"
"project," "expects" or similar expressions. These statements are made pursuant
to the safe harbor provisions of the Private Securities Litigation Reform Act of
1995. Forward-looking statements inherently involve risks and uncertainties that
could cause actual results to differ materially from the forward-looking
statements. Factors that could cause or contribute to such differences include
factors detailed in the sections entitled "Management's Discussion and Analysis
of Financial Condition and Results of Operations -- Risks Factors," "Factors
That May Affect Future Results and Financial Condition" and "Factors That May
Affect Future Stock Performance" in Ugly Duckling Corporation's most recent
reports on Form 10-K, Form 10-Q (including Exhibit 99 to any such Form 10-Q),
and Form 8-K, factors detailed in the section "Risk Factors" in Ugly Duckling
Corporation's definitive proxy statement dated August 4, 1998, and elsewhere in
Ugly Duckling Corporation's


                                       
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Securities and Exchange Commission filings. By making these forward-looking
statements, the Company undertakes no obligation to update these statements for
revisions or changes after the date of this press release.

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