Last December, 400 blank airline tickets disappeared from the office of Diplomat Travel Service in downtown Washington. The owner, Michel A. Mamlouk, reported the loss to police and then waited to see what would happen. It wasn't long before the nightmare began.

So far, 46 of the tickets have been filled out and turned in for refunds or used for travel within the United States and to such cities as Nairobi, Brussels, Tel Aviv and Paris. The airlines have billed Diplomat about $50,000 for these tickets, and Mamlouk fears that before it's over, the total will reach $400,000.

Many airline tickets, when properly filled out and validated, are as good as cash, and anyone who loses a ticket could find himself -- in a smaller way -- in Mamlouk's position. A spokesman for the Air Transport Association, which represents the airlines, said 53,000 airline tickets were stolen or reported missing last year at a probable cost to the industry of $1.8 million.

In the first six months of this year, the spokesman said, 8,488 tickets were stolen from 57 of the nation's 20,000 travel agencies, a fourfold increase over thefts from travel agencies in the same period the previous year.

"There's no way I can pay these things," said Mamlouk. "The airlines don't seem to care . . . . They're equipped to track down [stolen] tickets and they're not doing it. They're trying to collect from me."

Spokesmen for the airline industry said that while vigorous efforts are made to track down stolen tickets and prevent their fraudulent use, time constraints make it impossible to check every ticket that is presented at airline ticket counters immediately before or after flight times against a master list of stolen or missing tickets in airline computers.

"You got a wide-bodied plane and a line a mile long. They're so bogged down at the counter" that agents can't check the validity of each ticket, said Ernest Dunham, director of loss prevention for Eastern Airlines.

Dunham said that it would take "several seconds, not just two or three" for an agent to enter into a computer the multidigit identifying number that appears on the top right of each ticket, and for the computer to "read" that number against the master list of the numbers of tickets that have been reported stolen.

"It's just too big a load, and the agents are too heavily burdened," said Jerry W. Cosley, TWA's vice president for public affairs. "The lines are long enough," said United spokesman Chuck Novak.

What the airlines do, the spokesmen said, is to provide agents at check-in counters with a profile of traits for detecting suspicious persons. In addition, agents learn to spot tickets that are not made out properly. The airline spokesmen said the various codes and validating stamps used on all airline tickets make it difficult for them to be fraudulently used unless the holder has intimate knowledge of ticketing procedures.

"At the time of check-in, our people have been instructed to look for various peculiarities about a passenger coupon," said James Arey, director of public relations for Pan Am. "I can't say publicly what they are, but unless something like that stands out, the volume that you deal with means that you cannot run a computer check on each one . . . . Our agents are trained to be on the lookout."

Air Transport Association spokesman William E. Jackman said that millions of airline tickets are in circulation on any given day, and that in a recent month the ATA--which sends blank tickets to travel agencies on behalf of most of the nation's 140 airlines--distributed 16 million tickets to agents, a use rate of about a half million a day. In Mamlouk's downtown office alone, about 400 tickets are written each week. He also has branches in McLean and Reston.

Once an agent for an airline spots something suspicious, he punches the ticket number into a computer and compares it with the "blacklist" of stolen tickets.

None of this, however, has kept Mamlouk from receiving a steady stream of bills from the airlines for the stolen tickets as they continue to be used. He said his insurance does not cover the loss and the airlines have judged him liable for the tickets in part because they were stolen after one of his employes left them overnight on top of a filing cabinet.

"They say I haven't exercised due caution," he said. He disagrees with this assessment, saying that the process used by the airlines to deliver the tickets to him late in the afternoon at a time when he can't place them in a bank safety deposit box was the reason they had to be kept overnight in his office.

"They the airlines never check to see if it's a stolen ticket or a good ticket," said Mamlouk. "They should check all ticket numbers, absolutely. The whole industry should do it. It's that simple."