Left-winger Andres Manuel Lopez Obrador has a clear lead in the race to be Mexico's next president, exit polls said. The first official results were expected shortly.
The former mayor of Mexico City, who was the front-runner ahead of the vote, is estimated to have polled at least 53 per cent, one survey by Parametria said.
All exit polls put him well ahead of his nearest rivals, the BBC reported.
Delivering early and clear acceptances of their defeats, the two main challengers have recognised the winner.
Ruling party candidate Jose Antonio Meade conceded defeat and said he accepted Lopez Obrador has won and wished him well.
Meade's Institutional Revolutionary Party (PRI) has dominated Mexican politics for much of the past century.
The candidate for the conservative National Action Party (PAN), Ricardo Anaya, has also conceded and said he had called Lopez Obrador to congratulate him.
Sunday's election followed one of Mexico's deadliest campaigns in decades with more than 130 political candidates and party workers killed, the BBC said.
Lopez Obrador and his supporters have been waiting since 2006 -- the first time he stood for the presidency in Mexico. This was his third attempt.
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