Representatives of 21 airlines seeking the right to operate out of Washington's National Airport this fall completed their 13th day of deliberations yesterday without resolving the increasingly difficult issue of how the limited hourly operations will be divided among them.

But they were close, according to some participants, and will try again today.

Their work, if successful, will distribute the 640 slots currently available at National into hourly periods of 40 each during the airport's limited operating hours and determine which airlnes get them. A slot is industry parlance for an allowable movement of a plane -- either a takeoff or a landing.

Although the total number of slot requests will fit into the allowable maximum, right now too many airlines want to have their flights take off or land in peak hours -- primarily between 5 p.m. and 8 p.m. And the process of getting the airlines to "slide" their flights out of those hours appears to be a painful and difficult one for them. Each slide of a flight to an earlier hour or a later one affects other cities' schedules, crew times and aircraft utilization and generally disrupts a schedule an airline thinks may be profitable for it.

If the problem of too many airlines seeking too few slots already is aggravated, an even more difficult tasks lies ahead. Although the government-sanctioned airline committee generally works to set schedules for six-month periods corresponding to the beginning and end of daylight savings time, the committee has bought time in the current negotiations by trying to settle the time period running from Oct. 26 through the end of November only. For the period beginning in December, the committee must fit in at least 28 more slot requests: 24 from New York Air, an affiliate of Texas International Airlines, which seeks to begin low-fare Washington-New York service with them, and four from Air North, another new entraint into the airport.

In addition, the problem will become even more severe in January when the Federal Aviation Administration implements its new policy for National which reduces the number of commercial flghts per hour and imposes a stricter curfew on flights. As a result, the number of allowable slots for the major commerical airlines will be cut by 118.

Although some commuter airlines will move into a new category under this policy and not be eligible to participate in the committee's allocation, the slots they account for will not alter the problem significantly.

"Under the new policy, we're going to have to cut our existing schedules by 20 percent," one airline executive complained. "We're going to have to drop service to some cities we've served for years."

In case the committee cannot settle the slot allocations, the FAA is preparing to take over the task on an emergency basis, but FAA officials say they have not decided on a plan for doing so. During the last two days of meetings, some airline representatives have charged that others are failing to agree to slides to position themselves in hourly periods they like best just in case the committee fails to reach agreement and the FAA takes over.