NEW YORK (AP) _ A federal appeals court reserved ruling on a request by unionized workers at four metropolitan area commuter railroads to overturn a ban against their striking in sympathy with Eastern Airlines employees.

Lawyers for the railroads argued Tuesday before the three-member panel of the 2nd U.S. Circuit Court of Appeals that the Railway Labor Act requires the railroad employees to stay on the job until they go through a series of mediation steps.

Until the 2nd Circuit decides otherwise, U.S. District Judge Robert Patterson Jr.'s injunctions against sympathy strikes remain in force.

At issue is whether unionized workers at the Long Island Rail Road, NJ Transit, Metro-North Commuter Railroad and Amtrak may honor picket lines set up by machinists who struck Eastern on March 4.

Both the unions and the railroads agree that if all or most union workers honored the machinists' picket lines, the four railroads would have to shut down, throwing transportation facilities into chaos for more than 400,000 daily commuters in the New York metropolitan area.

On March 20, Patterson barred the railroad unions from honoring the picket lines and ordered union officials to tell their members to go to work if any picket lines went up at railroad facilities.

''We have been stripped of the most fundamental right that labor has: to withdraw its services and to call upon other workers to withdraw their services,'' Joseph Guerrieri Jr., lawyer for the unions, told the appeals panel.

He claimed that because the railroad workers have no dispute with their own employers they would not have to go through the numerous steps required by the Railway Labor Act before walking off the job in a sympathy strike.

But Bernard Plum, lawyer for the LIRR and Metro-North, said the Railway Labor Act encompassed all disputes and to claim workers could strike if they said there was no dispute ''defies logic.''