GRAPEVINE, Texas (AP) _ Leaders of American Airlines' pilots union met behind closed doors late into the night Tuesday to consider a new four-year contract that would end 16 months of unrest.

During the final day of the two-day meeting at a hotel at Dallas-Fort Worth International Airport, the 23 directors of the Allied Pilots Association went into a private executive meeting.

While the executive session was in progress, APA President Fred Vogel left the union's hotel room several times to meet with Robert Baker, executive vice president of operations for American.

The apparent difficulty to approve the contract comes after the union and the company heralded the pact reached Jan. 26. The tentative agreement ended six weeks of acrimonious discussions in which the airline accused pilots of staging an illegal sickout.

An unusually high number of American's 8,800 pilots called in sick during the busy December holidays. The APA denied the sickout charge, saying the company was blaming pilots for weather problems and poor scheduling.

Under the new contract, which would replace the one that expired more than a year ago, pilots would receive an immediate 8 percent pay raise, followed by 4 percent increases on Aug. 31, 1991, 1992 and 1993.

The new contract also calls for a reduction in the time it takes an American pilot to reach the company's highest pay scale, from nine to six years.

The pact reached with the help of a federal mediator leaves some issues to binding arbitration. Those include the pIlots' .ontribution to American's health plan and a retiree health benefits plan.