Watching Mexicans celebrating the end of 71 years of presidential rule by the same party was an awesome sight on Sunday night.

Joining them in their thousands at the Angel of the Revolution monument - the traditional venue for the post-election fiesta - meant being asked to blow plastic trumpets by unknown ladies, but this was Mexican history being made in front of your eyes, even if they were clogged with blizzards of shaving cream sprayed from aerosols.

The man of the hour - all six feet six inches of him - Vicente Fox, former Coca-Cola salesman and rancher, was on the platform, telling his jubilant supporters that "today Mexico is already different. Today Mexico enters the 21st century with its right foot forward."

It has been a dream victory for Fox, who was also celebrating his 58th birthday. Not only had he wrested the presidency from the ruling Institutional Revolutionary Party (PRI) but Fox's National Action Party (PAN) has also won the most seats in the two houses of parliament, though without securing an overall majority. It is not so long since PAN was a small, Catholic conservative party with its main support in the countryside.

It will take some time for all this to sink in as Mexico comes to terms with the rout of the PRI. This is the party which since 1929 has held the presidency by fair means or foul and whose ruthless political machine permeated every sector of society, including the police and army.

It is to President Zedillo's credit that when he took over in 1994 from Carlos Salinas, he set about ensuring fair elections for the future and set the economy on a stable course after a frightening start when the peso collapsed and bank failures almost ruined the country.

The big question today is whether the PRI will go quietly and ensure an orderly transition of power to Fox, who spent much of his campaign denouncing PRI corruption. It will be a long-drawn out transition as the new President does not take office until December 1st.

The signs were good on election night. Mr Fox acted the mature statesman, telling his supporters he wanted "a transition without rancour and without resentment". He paid tribute to Mr Zedillo for his swift acknowledgement of his victory and said they would be working together on next year's budget.

President Zedillo rose to the occasion, promising a "clean and transparent transfer of power". Mexico had proved by the defeat of the PRI that it had become "a mature democracy," he said in a televised address to the nation.

The defeated PRI candidate, a former minister, ambassador and governor, Francesco Labastida, and his supporters at PRI headquarters looked shell-shocked as 71 years of being top dog disappeared overnight. But he conceded defeat gracefully. The PRI will have a lot of time for the autopsy.

Mario Vargas Llosa, the Peruvian novelist and observer of Latin American politics, said after the election that now "we shall truly know what the PRI represents. We should see if it deflates as it loses all the power of the state or simply becomes an interest group lacking popular support."

Mr Fox, who has Irish and Spanish ancestry, now has a chance to reach out to all the opposition groups as he works to put together the coalition government he promised during his campaign. Without an overall majority in parliament, he will need a working alliance with the other parties to get new legislation passed.

His economic policies are a lot closer to the PRI than to the leftwing PRD of the third presidential candidate, Cuauthemoc Cardenas.

Fox had tried to make a pre-electoral pact with Cardenas to ensure the defeat of the PRI but had been rudely rebuffed and called a "traitor". Now Cardenas must decide if he can work with the rival he detests.

Fox, like Labastida, promised to improve education and fight the appalling poverty which still blemishes Mexican society in shanty towns outside cities and in rural areas. He aims to do this by doubling economic growth to 7 per cent and increasing exports which are already booming under the North American Free Trade Agreement with the US and Canada. A new free trade agreement with the EU has just come into effect, and Mexican oil is much in demand.

THE future President talks about a "common market" in 20 years between Mexico and the US, which would include freedom of movement, meaning Mexican emigrants could seek work freely in the US and not get shot or drowned or deported, as happens now when they try to cross the border illegally.

A more pressing priority is the fight against corruption in Mexico, which is linked to the pervasive drug culture and reaches to the highest levels of the police and even the army. Kidnapping of the rich, and even the not so rich, is alarmingly common, with armed bodyguards and electrified barriers in the affluent suburbs not always a defence.

Then there is the simmering revolt in the impoverished Chiapas region, which Fox once rashly said he could settle "in 15 minutes". Now he will be put to the test.

But there is no doubt he has swept the country off its feet by his forceful personality and swashbuckling campaign, conducted at times on horseback. He may have shot his mouth off at times but he knew how to reach out to the young people as well as to the business class with the promise of ending decades of deadening and corrupt PRI politics.

He has six years to carry out the "clean-up" he has promised after the 71 years of the PRI regime. He will encounter failures but many Mexicans will be grateful he had the courage to take on the PRI and make their country a real democracy.