Auto-Train Corp. resumed trading on the American Stock Exchange yesterday after the company announced an out-of-court settlement of claims against it by the Continental Illinois National Bank & Trust Co..

The hiatus in trading, which began June 11, ended shortly before noon with 1,600 shares opening at 3, down a half. By late afternoon the stock was trading a 5,200 shares, off three-quarters.

Sale of the stock had been halted pending an announcement which turned out to be the settlement with the Illinois bank. The bank had sought damages and repossession of 11 locomotives and 10 passenger cars leased to Auto-Train, which transports cars and their passengers by rail.

Although the settlement allows trading in the company's stock to resume, problems continue to cloud the future -- including the possibility that the company's stock may be delisted.

Under the terms of the settlement, Auto-Train agreed to pay Continental Illinois Leasing Corp. $450,000 in five month installments from July to November. Those payments are in addition to the company's regular monthly payments to Continental Illinois Leasing of between $48,000 and $65,000. Auto-Train was $650,000 in debt to Continental as of last Dec. 31.

Auto-Train also said it has secured an irrevocable letter of credit of $400,000 which can be drawn against by Continental Illinois if Auto-Train defaults. Auto-Train's senior vice president and chief operating officer, Ricahrd A. Goldstein, would not say from whom the letter of credit was secured.

Continental Illinois had charged in its suit that Auto-Train had failed to live up to an April agreement outlining how Continental would be repaid. Continental had also charged that Auto-Train had failed to maintain and repair leased railroad equipment. Under the settlement, Auto-train has until Sept. 30 to "undertake a cure" for maintenance defects.

In announcing the settlement and saying it would seek a resumption in trading, Auto-train conceded that the company does not currently meet all the Amex guidelines for continued listing of the stock. But the company noted that the exchange recently decided, after a meeting with company officials, not to move forward with delisting at this time.

The company's continued listing is subject to ongoing review.

On June 12, an Auto-Train subsidiary, Railway Services Corp., filed an offering statement with the Securities and Exchange Commission proposing to sell 600,000 shares of its stock. Under the offering, Auto-Train would sell 800,000 shares of Railway Services through a rights offering to Auto-Train holders. It the offering were successful, Auto-Train would raise $2.25 million from the sale of its shares and still retain 59 percent of the stock. Out of the money Railway Services raised, it would repay $800,000 to Auto-Train.