Last July, Alvin Kotz, a convicted gambler who lives in the Washington area, took some of his friends and flew to Las Vegas for $2,248. He stayed at Caesars Palace and used $4,000 of a $10,000 line of credit.

That intrigued government prosecutors, because Kotz had been telling them that he could not pay a $5,000 fine levied in 1973 in a bribery and gambling conviction. He had said he could pay only $10 a month -- because of his "aging Italian parents" -- and over six years, he actually had paid only $40.

Kotz, recently pleaded guilty to contempt of court for a "willful" failure to avoid paying a criminal fine. His conviction -- the first of its kind -- is part of a new government crackdown on criminals who have managed to avoid paying their fines.

In the District of Columbia alone, $647,000 in U.S. fines remains to be collected. Nationally, the total is $78 million and growing as more judges impose fines rather than send criminals to jail in federal cases.

Fines often are levied in high-profit crime cases, such as narcotics and gambling, and increasingly for white-collar crimes, but 40 percent of the fines imposed in fiscal 1977 and 1978 have not been paid in full, according to Ronald Roos, the Justice Department's criminal fine collection supervisor.

The fines usually go uncollected, according to interviews with several persons familiar with the criminal fine system, because judges too often impose unrealistically high fines on defendants who have few assets and because judges seldom get involved in setting up schedules for fine payments. In addition, the system has virtually no mechanism to vigorously seek and collect the outstanding amounts.

A computer printout of the unpaid fines in Washington shows a wide range of criminal defendants fined for a wide range of illegal activities over the past three decades. Some of those with outstanding fines are still in prison, others are presumed missing or dead and others are appealing recently imposed fines.

The printout also shows items such as these:

Former White House aide G. Gordon Liddy, who was fined $40,000 by U.S. District Judge John J. Sirica for his role in the Watergate break-in, has paid only $3,051 of that amount -- reportedly the value of the life insurance policy that he declared as an asset when he took a pauper's oath upon leaving prison.

Since that time, he has written a novel that is drawing wide public attention. Assistant U.S. Attorney Patricia Frohman said she was aware of possible income from the book, and added "We'll be back in touch with him."

Convicted pimp Sterling Godfrey, fined $35,000 in 1973, worked out an agreement with the U.S. Attorney's Office here in 1976 to pay off his fine at $10 a month, but has paid only $80 worth of his fine. Even if he paid the amount regularly, it would take him nearly 292 years to pay it in full.

A narcotics defendant identified in the printout as A. J. Hinton was fined $100 in 1953. Records in the U.S. Attorney's Office show that he was finally located 20 years later, paid $30 of his fine in 1973 and then dropped out of sight again.

Dr. Thomas W. Moore Jr., who is still in prison on drug-selling charges, has paid only $250 of a $70,000 fine. The U.S. Attorney's Office here has been told that Moore paid the high-priced Williams & Connolly law firm a "substantial amount" for representing him in his unsuccessful appeal of his conviction. In addition, the office has been told that Moore may have attachable hidden assets.

Assistant U.S. Attorney Donald E. Campbell, chief of the major crimes division, said that because his unit was successful in prosecuting Kotz, he intends to proceed against other "flagrant" abusers of the fine process. Campbell indicated that he would focus on gamblers and narcotics dealers whose sentences included fines.

The FBI office here also is monitoring some outstanding criminal fine cases to search for hidden assets or other signs that the persons could pay the outstanding amounts, investigators said.

Assistant U.S. Attorney Joseph F. McSorley, who handled the Kotz case, said he had sought a criminal contempt-of-court verdict in the case because it is a "punitive measure and is intended to vindicate the authority and dignity of the court." He said Kotz's actions in the case amounted to "blatant defiance" of the court's order to pay the fine in 1973.

Some judges have begun asking pre-sentence investigators to determine a defendant's ability to pay a fine before deciding whether to impose a fine or jail sentence. Others, however, still seem to impose fines in cases without determining in advance the defendant's ability to pay.

Persons familiar with the criminal fine process in federal courts said judges seldom set specific time limits within which a fine must be paid. In the D.C. Superior Court, they noted judges are more likely to give defendants a set period within which to pay any fine imposed, for example.

Roos said he believes judges are becoming more aware of the backlog of unpaid fines and are becoming "more reasonable" in levying them.

He pointed out that U.S. judges in certain areas -- Miami, New York, Detroit and Kentucky, for example -- are more likely to impose fines than in other areas.

Despite the problems with the system, Roos said he felt fines are a better deterrent than jail in many types of white-collar criminal cases and that the use of fines can relieve the overcrowding of prisons.

The Justice Department has recommended that U.S. attorney's offices around the country suggest to judges that they impose "stand-committed" fines, or fines that must be paid within a certain time or the person will be jailed, Roos said.

Federal judges here seldom attach such conditions to their fines. Instead, they often ask the U.S. Probation Office or the prosecutors to work out the details of the payment.

A clerk in the U.S. Attorney's Office here works with one assistant U.S. attorney in occasionally attempting to keep tabs on outstanding criminal fine cases. They attempt to contact defendants on a regular basis and ascertain their current financial status, according to Assistant U.S. Attorney Royce C. Lamberth.

If a defendant refuses to pay, liens can be placed on property or salaries attached. The prosecutors also can ask that the amount of the fine be deposited with the court pending any attempt to appeal a criminal conviction.

Prosecutors noted that it is difficult to attach salaries when defendants have no legitimate visible means of support -- a particular problem in gambling cases, they said.