A strong conservative challenge in two states along the U.S. border is threatening to crack the 55-year-old dominance of national and state politics by the Institional Revolutionary Party.

The showing by the right-wing National Action Party in the weeks prior to the July 7 elections has raised the question of whether a two-party political system is starting to emerge in at least one region of Mexico, with possible national implications.

Officials of the ruling party, known by its Spanish initials as PRI, say that opinion polls give it only a narrow lead over National Action in races for governors of Sonora and Nuevo Leon. National Action says that only fraud at the polls can deprive it of winning its first state offices, and that such fraud could spark rioting by party sympathizers.

Overall, the political power at stake in the elections is relatively small. National Action seems to have a reasonable chance of winning governorships only in Sonora and Nuevo Leon, out of the seven states where elections are being held. The country has 32 states. The PRI, while facing the possible loss of a few deputies in national legislative elections on the same day, is certain to retain its overwhelming majority in Congress.

But a conservative victory in a governor's race would carry great symbolic importance, according to politicians, professors and diplomats here. By ending the PRI's monopoly on control of state governments, it would challenge the bedrock assumption of Mexican politics that elections serve to reconfirm the PRI's right to rule rather than to give voters a realistic choice over who governs them.

National Action congressional victories, considered possible in several northern states and in Mexico City, also would boost the opposition's morale even while meaning little in terms of controlling Congress.

"What's important is not that the opposition wins one or two governships. What's important is that the PRI is losing its grip, and thus that the government is losing its grip," a political scientist at a Mexican college said.

The PRI has provided all presidents and senators, as well as governors, since it emerged as the "official" party in 1929 after nearly two decades of revolution and civil strife. Mexico has enjoyed political stability since then, at the price of effective political choice.

In recent years, the PRI has tolerated and even promoted formation of small rival parties to the right and left, but the PRI also makes clear that under Mexican democracy these groupings generally are to be heard rather than elected.

"Mexico doesn't have the maturity, the education for a two-party system," a senior Mexican government official said.

Dissatisfaction with the country's economy and with governmental corruption has boosted National Action to a position in the north such that it threatens the PRI's hegemony on a regional level. PRI sources said that they were particularly concerned about the governor's race in Nuevo Leon and congressional races in another border state, Chihuahua.

Several diplomats, professors and other observers suggested that the government might take extraordinary steps to keep the PRI in power in Sonora and Nuevo Leon. Irregular vote counts have a long tradition in Mexico, but charges of fraud this time could lead to more trouble than usual because of the danger of popular unrest.

In events that were widely interpreted as a preview of the July elections, National Action supporters rioted in the border town of Piedras Negras on New Year's Eve to protest what they charged was the PRI's theft of the mayoralty election there. They set fires that gutted the town hall and the police station and battled police for six hours with firearms, rocks and bottles.

"If there is fraud, there could be serious conflicts. Look at Piedras Negras," National Action spokesman Gonzalo Altamirano said, adding that the government's handling of potential opposition victories in the July balloting was "the great unknown."

Fraud accusations would be particularly embarrassing to the government of President Miguel de la Madrid as it approaches the midway point, at the end of this year, of its six-year term. He repeatedly has promised clean elections as part of his program of "moral renovation," but said last week that the country could not allow power to pass to "old and new oligarchies" that favor "a political change."

In addition, influential factions in the PRI are believed to wish to protect their power base even at the price of some bad publicity for the president.

"I think there is a tug of war within the PRI over what degree of tampering will be allowed," a senior, non-Latin diplomat said. "The state governments are not under the thumb of the central government on the electoral process as much as on policy matters."

National Action has the strength to threaten the PRI on the state level only in the north, where it has increased its power steadily in recent years with a series of victories in mayoralty races. Distance from Mexico City and closeness to the United States have encouraged a spirit of regional independence, and the drastic devaluation of the peso beginning in 1982 has had great impact along the border.

The party -- largest by far of eight opposition parties participating in the elections -- draws support primarily from business people and the urban middle classes. They are attracted in part by its procapitalist stance that contrasts with the PRI's fostering of a sizable public sector.

But most observers agree that National Action has gained strength more from protest votes against the PRI and against "the system" than from what the opposition espouses. The PRI is quick to emphasize that National Action offers virtually no coherent program, apart from criticism of the nation's economic difficulties and of corruption.

The PRI has tried to prevent National Action victories. In the industrial state of Nuevo Leon, for instance, it installed as the current governor a politician who is very conservative by PRI standards. Under his term, federal government funds have helped to rebuild a large chunk of the downtown of the state capital, Monterrey.

Senior PRI officials also warn regularly that National Action would sell out the country's interests to two traditional PRI antagonists: the country's Roman Catholic clergy and the United States.