Shows like The Phantom of the Opera have been hit

The strike is the result of a dispute between the American Federation of Musicians and Broadway producers who want to cut the size of some orchestras.

Losses from a fourth night of closure will be limited as most Broadway theaters are shut anyway.

There were no negotiations on Sunday and no sign of talks starting in the near future.

Both sides in the dispute have accused the other of failing to compromise.

"It's very difficult to engage in a negotiation when you don't have a negotiating partner... somebody who wants to bargain toward a compromise," said Jed Bernstein, who represents producers.

Bill Moriarity, union president, was equally pessimistic.

"We are right now faced with what the producers have termed a final offer.

"As long as the offer is 'final', it is difficult to negotiate against it."

Theatres had planned to go ahead with performances by using recorded music, but actors and stagehands refused to cross musicians' union picket lines.

Missing musicals 42nd Street Les Miserables The Phantom of the Opera The Lion King Rent Hairspray The Producers

It has led to the closure of practically every big musical show - and severe disappointment for US visitors and overseas tourists.

One estimate put the cost of lost business throughout the weekend at more than $7m (�4.4m).

Theatre workers held a rally on Sunday afternoon on west 42nd Street in the heart of Manhattan's theatre district.

Picketing was held in front of each darkened theatre about an hour and a half before the curtain went up.

Lucille Decristofaro, who sang in a Broadway production of Les Miserables, said: "Who wants to sing karaoke?

"The whole point of Broadway is live music, a sound you can only get live."

Jonathan Dinklage, who plays violin in Thoroughly Modern Millie at the Marquis Theatre, said: "We don't want more money. We just want to keep it alive."

Musicians fear they may be done away with entirely

Urging the two sides to resolve their differences, New York mayor Michael Bloomberg said: "In these challenging times, the darkening of Broadway casts a long shadow over the heart of the Big Apple."

The city is still economically vulnerable following the 11 September attacks.

Sean Ricketts, dining room manager at Sardi's restaurant, said the action was having a widespread impact.

"The restaurants, the hotels, actors and actresses, musicians, stage hands, taxi drivers, hot dog vendors (are affected)," he said.

"And millions and millions of dollars being lost, in a city already with a deficit of $3.5m. This is a very bad time."

Cabaret is the only Broadway musical still on stage, due to its separate arrangement with the union.

New York's economy remains vulnerable

Non-musicals and off-Broadway plays are still in business.

Under the current contract, musical productions currently must employ a minimum of 26 musicians - a number the producers want to reduce to about 14.

The union says it is concerned that producers want to phase out their services altogether and use recorded or computer-generated music instead.