(Adds details, quote from union leaders, company context)

By Teresa Cespedes

SANTIAGO, Nov 22 (Reuters) - Workers for the two largest unions at Southern Copper Corp in Peru said on Wednesday they had started an indefinite strike, demanding a fair share of mining profits, while the company said the stoppage had not affected operations.

The unions, which together comprise more than 3,000 members, said workers at the company's Cuajone and Toquepala mines and Ilo refinery in southern Peru laid down their tools on Tuesday. Peru is the world's No.2 copper producer.

"The workers are protesting on the train track that transports copper concentrate from the mines to the refinery so that they will listen to our demands," said Fidel Roman, head of the Unified Union of Workers, the company's top labor group.

The Toquepala Workers Union, the company's second largest with 850 members, also joined the strike.

Police had arrested 24 workers and injured three others after dispersing union protestors with tear gas and rubber bullets, Roman told Reuters.

Workers with three smaller unions had chosen not to strike, union leaders said.

Southern Copper Corp, owned by Grupo Mexico , said in a statement to Peru's market regulator that workers had started to strike at midnight (0500 GMT) on Tuesday but that it had not affected normal mining operations.

Southern Copper's mines in Peru produced some 310,000 tonnes of copper last year, according to government data. The strike is the second to hit Southern Copper's mines this year, following a two-week walk-off in April that ended after workers reached a deal with management. {nL1N1HW130}

The stoppage comes near the end of a turbulent year in labor relations at mines in South America, including disruptions at Peru's biggest copper mine, Cerro Verde, and Chile's Escondida, the world's largest copper mine. (Reporting by Teresa Cespedes, Writing by Dave Sherwood, editing by Louise Heavens and Cynthia Osterman)