Auto-Train Corp. applied yesterday for a $5.75 million federal loan guarantee and asked the Federal Railroad Administration for fast action on the request for aid.

The Washington railroad, which filed for bankruptcy in September, needs a government-guaranteed loan for operating funds and to repair and maintain its rolling stock, said Murray Drabkin, the trustee appointed to run Auto-Train.

A group of Washington investors recently loaned Auto-Train $400,000, but the railroad needs substantially more money to continue operation of its trains that carry passengers and their cars between suburban Lorton and Sanford, Fla.

If Transportation Secretary Neil Goldschmidt approves Drabkin's request for "expedited consideration," Auto-Train could get the loan within 15 days. Company officials have been working with DOT officials for several weeks on the loan application.

Since Drabkin was appointed by the Federal Bankruptcy Court to oversee Auto-Train, he has ousted the firm's top executives, laid off a quarter of its employes, closed down a rail car repair subsidiary and kept the trains running.

The Securities and Exchange Commission is investigating former Auto-Train chairman Eugene K. Garfield in connection with the collapse of the company that Garfield founded a decade ago. An earlier SEC investigation gave Garfield and the company a clean bill of health.

Auto-Train filed for reorganization in bankruptcy immediately after the SEC disclosed that a firm with which the company was negotiating a loan was run by two convicted swindlers.

The Washington Post later revealed Auto-Train had sought financial help from a Las Vegas casino linked to organized crime and the Teamsters union pension fund and had hired a convicted felon as a financial adviser.

The SEC is probing at least one additional Auto-Train deal involving a Caribbean bank that was supposed to provide funds for the railroad, sources familiar with the government investigation say.

Immediately after taking over the railroad, Drabkin canceled an arrangement with a New York firm that was supposed to be providing Auto-Train with cash in exchange for tickets on the train. Drabkin said the firm was unable to account for all the tickets.

Drabkin has told the bankruptcy court that Auto-Train's records are in shambles, and he has not yet determined how much the company owes its creditors.

By filing for reorganization, Auto-Train is able to postpone settling its old debts while Drabkin attempts to restructure the company so it can operate profitably.

The trustee recently arranged to lease four locomotives from Amtrak and has obtained extra spare parts so damaged cars could be repaired and put back in service. Using the refurbished cars, he recently expanded each Auto-Train from 32 rail cars to 40.

Auto-Train runs a tain in each direction daily five days a week. The southbound trains are running at full capacity every day, a spokesman for the trustee said.