The ruling Institutional Revolutionary Party, known by its Spanish initials, the PRI, has held the presidency for the past 71 years without a break - longer than any other party in the world.
However, polls say the opposition has its best chance ever to break the PRI's grip in this weekend's elections.
The PRI presidential candidate, Francisco Labastida Ochoa, takes his party's legacy seriously and will not go without a fight.
The last thing Mr Labastida wants is to be remembered as the man who lost that power.
The party, therefore, has been resorting to various tactics to maintain its position.
But millions of people, including the party's hardcore - poor indigenous farmers - have been left out of the country's current economic boom.
Disillusionment
Many are deeply disillusioned with the PRI. Hundreds walked out of a recent campaign rally during the candidate's speech.
It is a danger signal to the party that needs every vote it can get.
Vincente Fox of the National Action Party, or PAN, is the man leading the assault on the PRI's once-dominant position.
He is a former Coca-Cola chief executive who has struck a chord amongst the middle classes fed up with decades of rampant corruption, alarming crime rates and a system of political patronage.
Sudden computer problems
However, the PRI is notorious for doing whatever it takes to maintain power.
During the 1988 election, the PRI interior minister announced the electoral computers had crashed, just as opposition leader Cuauhtémoc Cardenas was leading the count.
Fraud was never proved, but the country came close to revolution. Most Mexicans believe the election was stolen.
Open fraud on election day is not likely this time, as Jacquelline Peschard of the newly formed Federal Electoral Institute explains.
"That is why we are not concerned about that," she says.
When the computers were restored, Mr Cardenas was behind.
"What we are really concerned about is what comes up around the elections, not what has to do with the electoral process or the organisation of the election."
"It's not blatant ballot-tampering, but rather voter manipulation that's a threat to free and fair elections this time around."
Voter manipulation
Several weeks ago, a channel carrying raw sewage from Mexico City burst, flooding the town of Chalco with millions of litres of foul water.
1946: Party renamed Institutional Revolutionary Party
1988: PRI loses 48% of its seats in the lower house
Mar 1994: Presidential candidate Luis Donaldo Colosio assassinated
Sep 1994: Secretary-general Jose Francisco Ruiz Massieu assassinated
Dec 1994: Ernesto Zedillo inaugurated as president
Jul 1997: PRI loses control of lower house - first time in 68 years
"They told us that they could fix the canal quicker with the support of our vote," one woman said.
"That means they are taking advantage of this disaster. That way they pressure us. It's not fair."
It seems to be just one example of the party's dirty tricks in its struggle to hold on to power. There are persistent reports of blatant attempts at vote buying, or of coercion.
However, Carlos Almada, the PRI campaign director, insists the party is doing everything within the law.
"Some of the things you mentioned are not illegal. We will do everything within the legal framework," he says.
Rural campaigning
However, one party worker directly involved in the campaign tells a very different story.
"Beyond campaigning there is a lot of corruption, mainly in the rural areas where the majority of people are ignorant, and you can easily buy them with food, or even money," he says.
"Those votes go directly to the PRI."
A more subtle form of influencing the vote involves Mexico's rural assistance programme, Progresa.
The government has spent huge sums of money on advertising campaigns to promote its achievements, implying that if the PRI does not win, the assistance will disappear.
The party insists that everything is above board.
Rojelio Gomez Hermosillo of the watchdog, the Civic Alliance, says that that is not the issue.
"The issue is if their promoters in the field are telling poor people, illiterate people, that if they don't vote for the PRI that they will be out of this programme, that is very different thing," he says.
The opposition has been accused of similar scare tactics.
However, the fact that the PAN has no real power limits what Vincente Fox can do to combat the PRI machine.
He is trying hard to maintain the moral high ground, but it is an uphill battle.