About 70 workers walked off the job on Tuesday over a stalemate in contract negotiations with APM Terminals, which operates Pier 400. Other dockworkers are honoring the strike, and the pier remains shut down Wednesday morning.
The Port of Los Angeles is the nation's biggest cargo port. The strike has brought work to a halt. The strike has also stopped work in at least half the terminals at the Port of Long Beach.
Workers walked the picket line Wednesday at Pier 400, the biggest and busiest cargo terminal.
Late Tuesday night, an arbitrator ruled the strike was illegal and ordered strikers to return to work.
The clerical workers are from International Longshore and Warehouse Union Local 63. Their previous contract with APM Terminals expired in June of 2010. Contract talks broke down because workers claim management is trying to outsource jobs overseas.
Negotiators for the shipping company say no jobs have been sent overseas and APM Terminals has offered the workers absolute job security.
Port police said there has been no violence and no arrests.
The Associated Press contributed to this report.