As political second acts go, the victory on Sunday of Mexico’s Institutional Revolutionary Party is striking. The PRI ruled Mexico with a corrupt hand for 71 years, until it finally lost the country’s presidency in 2000. At the time, its plunging fortunes seemed to herald a new era of multiparty democracy.

Now, though, amid voter anger over drug violence and economic malaise, the PRI is back. But the onus will be on the president-elect, Enrique Pena Nieto, to prove that the party has adapted to modern democracy.

Pena Nieto, a state governor and the husband of a popular telenovela actress, says the PRI’s days of vote-rigging and graft are behind it. He has also pledged not to cut any deals with organized crime; in the past, the party has been accused of a wink-and-nod relationship with the nation’s drug cartels, trading lax enforcement for peace.

Those are all welcome promises. But there are troubling signs that the party’s habits haven’t died away completely. During the campaign, a British newspaper uncovered documents suggesting that the PRI was buying favorable TV coverage from Televisa, one of the nation’s most powerful broadcast networks.

The PRI seemed to hold a nostalgic appeal for some voters, who have been disenchanted by the incumbent president, Felipe Calderon, and his predecessor, Vicente Fox, who broke the PRI strangehold in 2000. If the president-elect can stem the drug violence that has claimed 55,000 lives and recharge the Mexican economy, both sides of the border will benefit. But Pena Nieto needs to be sure that in tackling the nation’s new nightmares, he doesn’t relive its old ones.