Many Washington area travel agents are advising travelers not to buy an Eastern Airlines ticket in light of the airline's financial troubles, the uncertainty of a strike and Texas Air Corp.'s announcement yesterday that it is buying the beleaguered airline.

"Up until today, I would have booked a person on Eastern and a backup flight, which is usually more expensive, on another airlines," said Larry Frommer, president of Frommer Travel Service on 17th Street NW. "But from this point on -- until we know something certain -- I would advise people to just book on another flight."

"We're trying to avoid booking on Eastern whenever possible," said Guido Adelfio, manager of Bethesda Travel Center.

Although Eastern officials affirmed yesterday that they intend to keep flying, they could not give any definite answers about how frequent-flyer programs and Eastern tour packages would be treated in the future.

Some travelers, however, are opting for the less-expensive Eastern tickets with the announcement of Texas Air's acquisition of Eastern.

One District resident, Stewart E. McClure, wasn't going to let the confusion about Eastern's future change his plans to take the less expensive flight on his vacation this week.

McClure bought an Eastern ticket yesterday for a flight to Martinique that is scheduled to depart Wednesday afternoon. "The way it looks now, unless something drastic changes, it looks like the flight will proceed on the basis of the news today," McClure said.

Eastern is a major carrier from Washington to the Caribbean and provides the only direct service to Bermuda, the Bahamas and San Juan, Puerto Rico, according to area travel agents.