MORELIA, Mexico (AP) _ Millions of Mexicans voted in local elections across six states Sunday, testing the battered popularity of Mexico's ruling party amid a severe recession that has wiped out more than 1 million jobs.

Exit polls showed the governing party leading the biggest race, for governor of western Michoacan state, but trailing conservative foe National Action in the bitterly fought mayoral race for the central city of Puebla.

National Action claimed it was also showing strongly in mayoral races from Oaxaca City in the south to Mazatlan on the Pacific Coast and Culiacan in the north. Its supporters were jubilant even in the absence of first official results not expected until later Monday.

National Action supporters honked horns and celebrated in Puebla's streets as their mayoral candidate, Gabriel Hinojosa, declared triumphantly, ``I already feel like the mayor.''

Mexico's governing party refused late Sunday to concede Puebla.

But an exit poll of 1,460 voters in Puebla found National Action leading that mayoral race 50.2 percent to 38.6 percent. The University of Guadalajara's Center for Opinion Research, which conducted the poll, said it had a margin of error of 5 percentage points.

In Sinoaloa state, even ruling party Gov. Renato Vega Alvarado recognized ``a clear and favorable tendency toward National Action'' in both the state capital of Culiacan and the Pacific port of Los Mochis.

The voting was mostly peaceful, but two deaths were reported in the southern state of Oaxaca. Party officials said a member of the ruling Institutional Revolutionary Party was killed and two were injured in Mazatlan Villa de Flores, and the brother of an opposition candidate was shot to death in Asuncion Ixtaltepec.

Support for the ruling party, known as PRI, has dropped steadily since a severe economic crisis hit Mexico three weeks after President Ernesto Zedillo took office last Dec. 1.

Since then, the peso lost more than half its value against the dollar. Inflation soared from 7 percent in 1994 to an estimated 50 to 60 percent this year. Sales have dropped, and scores of businesses close every month.

``This election is a national plebiscite on the politics of the current federal government,'' Porfirio Munoz Ledo, chairman of the leftist Democratic Revolutionary Party, warned in a campaign speech.

The most closely-watched race was a tight, three-way battle for governor of Michoacan state. The state's 1.9 million voters also were choosing 113 mayors, and 30 state legislators.

Victor Manuel Tinoco Rubi, a former PRI federal legislator, was running against opposition challengers Cristobal Arias Solis of the Democratic Revolution party, and Felipe Calderon Hinojosa of the conservative National Action Party.

In the states of Puebla, Sinaloa, Tlaxcala, Oaxaca and Tamaulipas, a total of 6.6 million voters were picking mayors and state legislators.

In Morelia, the Michoacan state capital 135 miles west of Mexico City, a steady stream of voters passed through voting stations inside schools and colonial-era buildings. Scores of men in straw hats and women in shawls cast ballots in towns and villages around Michoacan.

In Mexico City, 5.4 million voters were choosing 365 neighborhood council members, new offices created to deal with local problems in the metropolis of 12 million. Candidates for city council were not allowed to belong to any political party.

Voter turnout was low until midday, when it started picking up. Tens of thousands of police guarded the polls, and there were only a few complaints of fraud or other irregularities after voting ended.

The PRI has stayed in power since 1929, through elections that critics say were marred by fraud, intimidation and bribery.

The party didn't lose an election for governor until 1989, when a candidate of the National Action Party won in Baja California. The party won again there this year, and now has governors in four states.

The close race in Michoacan could make it the fifth.

Michoacan is the home state of Mexico's most revered president, Lazaro Cardenas, a populist who gave land to the poor during his 1934-40 term.

His son, Cuauhtemoc, became governor, but he broke from the leading party in 1987 and established the Democratic Revolutionary Party. The ruling party has defeated every Democratic Revolution attempt to gain power.