This will not necessarily be wholly bad news for President Carlos Salinas de Gortari, who meets President George Bush in San Diego today to give a final push to negotiations on a North American Free Trade Agreement (Nafta). Some of the diehard opposition to the deal in the US has focused on the allegedly undemocratic nature of the Mexican political system, which has been dominated by the PRI since 1929.
The victor in Chihuahua was Francisco Barrio Terrazas, a 41- year-old businessman representing the right-wing National Action Party (PAN), who claims he only lost to the PRI candidate last time out, in 1986, because of massive fraud. The election was being seen as a test of Mr Salinas's proclaimed commitment to democratic reforms, and the ruling party's supporters will hail the result as proof of the changes that have taken place since Mr Salinas took office in 1988.
The PRI had been confident of victory in Chihuahua, after overhauling its local organisation and selecting a popular candidate, Jesus Macias, former mayor of the frontier boom town of Ciudad Juarez. But PRI officials recognised that the party was vulnerable in the prosperous north, where the economy is closely integrated with that of the US and the PAN is well organised - it also controls the western border state of Baja California. 'It's the first world up there, not the third,' a senior PRI official said recently, 'we couldn't rig things even if we wanted to.'
In Sunday's other gubernatorial election, in the central state of Michoacan, the PRI claimed to be well in the lead yesterday, provoking accusations of fraud from Cuauhtemoc Cardenas, leader of the opposition Party of the Democratic Revolution (PRD). The PRD, founded by PRI dissidents who regard themselves as guardians of the true spirit of the Mexican Revolution of 1910-17, had said beforehand that the PRI was planning to rob it of victory, and that it would call its supporters out on to the streets in protest if the result went against it.
Michoacan, a traditional agricultural state west of Mexico City, is the PRD heartland, and if it cannot win there it is finished. Mr Cardenas claims that he defeated Mr Salinas in the 1988 presidential elections, but was deprived of victory by fraud. His party has been going down hill ever since; the PRI won all 13 municipalities in Michoacan in local elections last year, and has been investing heavily in a backward state where more than a million poor peasants emigrate to California every year in search of work.
Mr Salinas arrives in London on Saturday for a four-day official visit, after which he travels to France, Spain and Hungary.