Mexicans will today know whether the 71-year-old hold on the presidency by the Institutional Revolutionary Party (PRI) has been broken by the challenge from Mr Vicente Fox of the opposition pro-Catholic National Action Party (PAN).
Yesterday about 40 million voters went to the polls to cast their votes for the PRI candidate, Mr Francisco Labastida; Mr Cuauhtemoc Cardenas of the leftwing Democratic Revolution Party; Mr Fox, and two minor candidates.
Voting continued in parts of the country until 2 a.m. this morning Irish time. Early exit polls had to be treated with caution as they could distort the final results in what is seen to be a close race between Mr Labastida and Mr Fox.
The new president will not take office until next December.
The stability of Mexico this time compared with the last presidential election in 1994 is striking. Then the PRI candidate, Mr Ernesto Zedillo was elected president after the party's first choice, Mr Donaldo Colosio was murdered and Zapatista guerrillas had begun a rebellion in the poor, remote state of Chiapas.
The election is being closely watched by the US which has extensive economic interests in Mexico. It is also the second largest trading partner of the US following the success of the North American Free Trade Agreement (NAFTA) signed almost 10 years ago.
Some observers fear that a narrow win for Mr Labastida could lead to claims of a rigged election, nervousness by foreign investors and a weakening of the peso. But others point to the strength of the Mexican economy compared with six years ago and the preparations made by President Zedillo and the Central Bank this time to prevent a collapse of the currency or a flight of foreign investment.
This election is regarded as the fairest in Mexico's history. Almost 1,000 foreign observers monitored the voting and the count around the country's 113,000 polling stations. There were also about 10,000 observers from Mexican organisations.
While doubts were expressed about how such a large election could be adequately monitored, the independent Federal Election Institute (IFE), which has spent $1 billion preparing for the day, was confident fraud would be virtually impossible.
Each polling station had registered officials from each party closely watching the voting. There were transparent ballot boxes and voters had to produce photo identification.
The former US president, Mr Jimmy Carter, who is in Mexico as an observer, said that while he did not regard Mexico as a democracy 10 years ago, "I feel very good about the progress towards true democratisation."
While the voting and count were seen to be reasonably free of fraud, it was difficult for the IFE to deal with allegations of "vote coercion" in rural areas.
The PRD is likely to retain the government of Mexico City, according to exit polls broadcast by Televisa. The PAN appeared to have easily won gubernatorial elections in two states - the farm-belt state of Guanajuato and the central state of Morelos, according to early exit polls by local television stations.