Airlines operating at Washington's National Airport this week agreed to let Colgan Airways use some currently unused landing and takeoff privileges to begin new service from Washington to Hot Springs, Va., starting April 1.

But the airlines, which met in committees here this week, made no discernable progress toward resolving their more difficult problem of how to divide the limited space at National, New York City's LaGuardia and Chicago's O'Hare International airports among all the airlines in the summer season, which begins for them on April 27, when daylight saving time begins.

The airlines met in January but resolved summer operations for only New York's John F. Kennedy International Airport. They have agreed to come back again in March for a third round of negotiations.

The airline representatives meeting are members of government-sanctioned committees that have been hammering out slot agreements twice a year since 1968 for the four so-called "congested" airports. With the advent of airline deregulation, in the last two years new airlines have been created, and it has become easier for airlines to fly new routes -- making the committees' work significantly more difficult with each meeting.

While LaGuardia is a problem -- with 19 airlines seeking 870 slots at an airport which permits no more than 768 operations a day -- National is even worse. Although 640 operations a day by the commercial airlines now are permitted at National, that number is scheduled to drop to 522 on April 27 when a Department of Transportation plan for the airport takes effect.

Besides reducing the number of operations from 40 to 36 an hour, the plan also imposes a 9:30 p.m. curfew and allows the introduction of wide-body jets at National. But the total number of flights isn't reduced under the new plan, because commuter airlines will be allowed to pick up the four slots per hour the commercial airlines lose. Also under the plan, requests for slots from airlines using planes with fewer than 56 seats are removed from the airline scheduling committee's deliberations.

Taking into account the changes now scheduled, 18 airlines now are seeking 752 landings and takeoffs a day this summer when only 522 will be available.

Although the process of allocating slots is thorny enough, it has been complicaed this time because of the change of administrations. The Air Transport Association and officials of many of the airlines have urged Transportation Secretary Drew Lewis to delay implementation of the planned flight reductions and to undertake his own review of the National Airport policy.

While a DOT spokesman noted that a review of the policy has been started, he said it is part of the overall process of educating the new officials to DOT policies and programs. The review of the National Airport policy hasn't been started with a view to changing it, although it is impossible that a review could lead to a change, he said.