Parking spaces are expected to virtually disappear today at National and Dulles International airports, an airport authority spokesman said last night.

Use of the lots at Baltimore-Washington International Airport was reported to be heavy, but a parking official reported that there were no problems there last night.

Holiday parking crunches are not unusual at National and Dulles. However, after significant parking and traffic problems at the two airports around Thanksgiving and Christmas last year, airport officials added parking spaces, exit booths and valet parking at Dulles and began studying plans for more roads and parking structures at the two facilities.

Dave Hess, a spokesman for the Metropolitan Washington Airports Authority, which operates National and Dulles, said that only a few hundred spaces were available at each airport yesterday evening and that these were expected to be taken sometime today.

Officials are urging travelers intending to use the airports to avoid parking and traffic problems by taking public transportation. Motorists are reminded that they can drop off passengers in satellite lots, where shuttles will take them to the terminals.

For information on parking and traffic for Dulles, call 471-4242; for National, call 684-7766.

For information on parking and traffic at BWI, call 261-1000 from the Washington area or 859-8981 from Baltimore.

BWI, which has not reported parking problems during recent holiday seasons, has more than 10,600 spaces. Dulles has about 1,000 more parking spaces than does BWI, but it has recorded a significant increase in passenger use in the past 15 months.

During the 1986 Thanksgiving and Christmas crunches, airport officials broadcast radio warnings that all of Dulles' spaces were full and apologized for traffic jams at the exits that meant 30-minute waits.