NEW ORLEANS (AP) _ An FBI agent today detailed hundreds of thousand of dollars' in gambling debts run up by Gov. Edwin Edwards, as prosecutors tried to show a motive for Edwards' involvement in an alleged $10 million hospital scam.

Jerome DeFranco said Edwards, gambling in Nevada under aliases such as E. Lee or T. Wong, left at times with debts reaching a half a million dollars. According to DeFranco, most of the debts were paid off in cash.

Defense attorneys said that the debts were all paid off by the end of each calendar year, 1982, 1983, 1984. But prosecutors stressed that Edwards was required to file financial disclosure statements, first as a candidate for public office and then as governor, showing all debts incurred at any time of the year.

Before DeFranco took the stand, U.S. District Judge Marcel Livaudais told the jury that the gambling itself was not illegal. He also told jurors that the gambling debts were not evidence of Edwards' guilt or innocence regarding the alleged hospital scheme.

The evidence of gambling debts could be used only to decide whether Edwards had a motive for involvement in the allegedly illegal activities, Livaudais said.

Theodore Jones, who filled out the statements for Edwards, said under cross-examination today that Edwards never told him what to put in or leave out.

Jones went on to say that the governor didn't even read the disclosure statmements.

''He'd thumb through and say 'where am I supposed to sign' and he'd sign and I'd get out,'' Jones said.

The governor, his brother Marion, and seven others are accused of racketeering and mail fraud. Prosecutors say the men used their political influence to obtain valuable ''certificates of need'' for hospital and nursing home projects in which they held interests.

They then allegedly sold the certified projects to large hospital corporations and made about $10 million.

It was the first time the issue of the governor's gambling was brought up since the trial began more than eight weeks ago. In opening arguments, prosecutors said the governor ran up debts to Nevada casinos totalling about $800,000.

Edwards began filing the financial disclosure statements in 1983, while running for governor, and the first ones covered 1982. He took ofice in March 1984.