LAGOS, NIGERIA, DEC. 8 -- Millions of citizens of Africa's most populous nation today exercised a basic right that largely has been denied them since Nigeria's independence was gained 30 years ago.

They took part in seemingly fair and nonviolent elections to choose hundreds of local government officials throughout the country.

"This is a great day for Nigeria," exclaimed L. Adele Jinadu, a top official of the National Electoral Commission, a government body overseeing the nation's transition from the five-year-old military government of Ibrahim Babangida to civilian, democratic rule, promised to take place in 1992. "Democracy is on the rise."

At more than 200,000 polling sites throughout this land of 125 million people, the voters indeed spoke today -- but literally with their feet.

In an unusual effort to stamp out plagues of vote rigging and ballot box stuffing during two earlier and fitful attempts at democratic government, Nigerians took part in an open polling system by standing in lines behind paper portraits of their candidates. The candidates represented two government-formed political parties, the only two allowed to participate in the election.

The voters were then counted aloud one by one by electoral officials, who surely had to be among the most abused, embattled and overstressed citizens in all of Africa today. At many points in the capital and countryside on election day, voters shoved, shouted, bickered and cursed. It was, in short, a thoroughly Nigerian affair.

"You bloody idiot! Of course I have a right to stand here! I have lived in Lagos all my life," a dapper, elderly gentleman standing at the head of a voting line indignantly shouted at Borke Enaghu, the unlucky official in charge of making sure voters were properly registered and counted in a robust working class section of Lagos known as Obalende.

Enaghu tried his best to explain that everyone had to be properly registered beforehand to vote, and suggested that perhaps the old man had forgotten or neglected to. But the fellow, resplendent in a flowing robe, would have none of that. He angrily pushed the beleaguered official and thereby set off a wild chain reaction in which some voters standing in competing lines and waiting to be counted began to shove each other.

Furious oaths and howls of indignation filled the muggy air. Fortunately, this hubbub lasted only a moment or two longer, for Nigerian police were on hand in force to prevent any outbreaks of violence and murder such as those that marred many of Nigeria's previous elections. The police were among more than 80,000 security forces, backed by the military, providing security at the nation's polling places today.

Thus, within minutes, the elderly fellow was escorted from the polling site and the counting commenced, with Enaghu's voice ringing the air with shouts of "One! Two! Three!" as he strode up and down each line of voters.

This remarkable scene was repeatedly played out around the country today as Nigerians once again attempt to establish an elusive tradition of fair elections and democratic government after tragic past failures.

While today's exercise appeared largely peaceful, it also was highlighted by an unusually low turnout. In several polling stations today, fewer than 15 percent of registered voters bothered to visit the polls and choose a line to stand in. In the past, turnout has averaged 40 percent.

Still, occurring near the end of a year that has seen movements for democracy stir nations across Africa, today's elections in a country that proudly considers itself a cultural, intellectual and economic leader for the continent appeared to hold wider resonance.

"We have much to overcome. The developed world is far ahead of us," said electoral commission director Humphrey Nwosu. "But with experience we grow. Who knows? Perhaps in a few years we will zoom ahead of everyone."

This oil-rich country experienced two periods of popularly elected government, 1960-66 and 1979-83. Two-thirds of Nigeria's years of independence have been spent under military rule, while the years of civilian government were fraught with rigged elections, widespread official corruption and misguided economic policies that resulted in large-scale waste of the country's prodigious oil earnings.

The Babangida government, which came to power in a military coup in 1985 and inherited the task of imposing severe economic austerity measures to make up for the nation's decades of profligacy, has spent large sums of money in an effort to educate the public about democracy and to instill democratic traditions here. The effort is strongly supported by the United States and other Western governments.

Today's elections represented the first stage in the transition process, which also is scheduled to include statewide gubernatorial elections next year and national senate and presidential elections in 1992. Those elections are due to be held under secret balloting. The government has promised to turn over power to civilian leaders after the 1992 elections.

This democratic process has been marked by many changes in plan by the government, which, in an attempt to quash past corrupt practices in electoral politics, has banned scores of so-called old breed politicians from participating or running in the elections. The most stunning change in course occurred last year when Babangida outlawed a host of fledgling parties in favor of two established by the government.

The government then proceeded to write political manifestos for these two parties, the Social Democratic Party and the National Republican Convention, one described as "a little to the left," the other as "a little to the right."

This two-party system was modeled on the American political system, but in practice it reflects a distinctly Nigerian character. The logos of the SDP and NRC are a horse and an eagle, respectively, the two animals on Nigeria's official crest. While SDP advertisements trumpet promises of free health care, education and public housing with roofs for the common man, NRC ads vow to protect private enterprise while providing the people with more rudimentary needs: "food and water."

Whether this attempt to overlay an American democratic system on an African reality will succeed remains to be seen. Today's elections, whose results will not be revealed until next week, seemed as much a test of the nation's ability to simply stage a peaceful contest as of the voters' desires at the grass roots. The voters were electing council members and chairmen who decide local matters pertaining to schools and other public works.

The normally car-jammed streets of Lagos were deserted today, with no vehicles except essential ones allowed on the roads during voting hours. The government made sure that all polling stations were located within walking distance of voters' homes.

Prior to today's election, voters were urged in public pronouncements to eat a full meal before going to the polling stations, so as not to be "unduly induced" to vote one way or another by persons with food. Indeed, such basic desires seemed uppermost in most voters' minds.

"I have come because of my children," said Ganiyu Dada, a 31-year-old bricklayer who lives in Sango-Ota, a town in Ogun state, just west of Lagos. Dada pointed at the two-lane highway next to the polling station and said children in his neighborhood are frequently hit by speeding cars while crossing the road to go to school.

"I want a school on this side of the highway. I want a good councilman who will get us a school here," he said, explaining why he was voting today. "I don't want my children to be hit by the cars."