LOS ANGELES — Cargo ships were stacking up today at the ports of Los Angeles and Long Beach as a strike shut down most of the terminals at the nation’s busiest port complex.

About 70 clerical workers from the local chapter of the International Longshore and Warehouse Union were picketing seven of eight Los Angeles terminals and at least three of six Long Beach terminals, port officials said.

Dockworkers from the same union were refusing to cross the picket lines even though an arbitrator ruled the walkout invalid on Tuesday.

By this morning, at least 18 ships docked and inside the adjacent harbors were not being serviced, port spokesmen said.

“Basically, we’re not moving cargo in and out here,” Los Angeles port spokesman Phillip Sanfield said.

The clerical workers have been locked in a contract dispute with 14 shippers for 2 ½ years. Talks broke off Monday and the workers struck a single terminal but expanded the picket lines Wednesday afternoon.

No new contract talks were scheduled.

Combined, Los Angeles and Long Beach comprise the nation’s busiest port complex, handling 40 percent of the nation’s import trade.