In 1952, George Bush, then a young oilman in Midland on the West Texas plains, and his wife, Barbara, worked as poll-watchers during the state primary election. It was a historic occasion, the first-ever Republican primary in the district, but when the polling booths closed that day the tally on the Bush side of the room was pathetic.

"Three people voted Republican," the vice president recalled at the Texas GOP convention here over the weekend. "Me, Barbara, and one drunk who thought he was voting Democrat."

Republicans are fond of telling stories about their bleak past in Texas, for it is the past. In 1986, their party has finally reached parity with the Democrats. Polls show that about one-third of the state's registered voters now identify with each party, and Bush is not alone in predicting that the Republicans might soon become the majority in the South's most populous state.

Their candidate for governor, Bill Clements, is favored to recapture the state's highest office from Democrat Mark White, who had defeated him four years ago. And as another sign of strength, when their parties held their state conventions during the weekend -- the GOP in Dallas and the Democrats in Austin -- it was the Republicans who attracted most of the attention from reporters and national politicians.

The Democratic convention was a rather lifeless gathering attended by none of the big names among the party's presidential prospects. It began with the news that White had finally decided to call a special session of the legislature, probably in August, to deal with what now appears to be a $2.3 billion budget deficit. And it ended with White, bravely trying to repair splits in the coalition that got him elected, apologizing to the state's teachers for making them take competence tests to keep their jobs.

Things were different in Dallas. The convention here attracted not only Bush, a favorite son of sorts for the 1988 presidential nomination, but also Rep. Jack Kemp (R-N.Y.), Senate Majority Leader Robert J. Dole (R-Kan.), the wife of television evangelist Marion G. (Pat) Robertson and even dark-horse candidate Alexander M. Haig Jr., the former secretary of state, who claimed he was just passing through and heard there were a lot of other Republicans in town.

The main reason for the attention here, however, was not the presence of the big national names. It was because Texas Republicans, as they grow and gain strength, are experiencing the same types of internal struggles, the same difficulties trying to keep their coalitions together, as those that used to make the Democrats so colorful, if not effective.

Here the struggle was between mainstream Texas Republicans, already on the conservative side of the spectrum, and evangelical Christians further to the right.

The well-organized fundamentalists, many participating in state politics for the first time, took over dozens of district caucuses at which delegates to the convention were elected, and their strength in Dallas was thought to be about 30 percent to 40 percent. They pushed a candidate for party chairman, the Rev. Sam Hoerster of Austin, whose slogan was "God and Government," and a platform that included what was known as a "solemn covenant and oath" pledging all Republicans to a Christian God, free enterprise and low taxes. In the end, Hoerster and the solemn oath were defeated, but the fundamentalists had made their impact on the convention.

The largest rally here was staged Friday night by the Coalition for Traditional Values, at which singer Anita Bryant led the crowd in "God Bless America," and David Davidson, an evangelical who was nominated as the party's candidate for lieutenant governor, pronounced that "things are going to be right because Texas is turning to the right."

The platform eventually approved by convention delegates called for a quarantine of all acquired immune deficiency syndrome (AIDS) victims, declared that the state should have no role in regulating church and home schools, supported prayer in public school and opposed abortion in all cases except when the life of the mother was endangered.

"We got most of what we wanted," said Marvin Holland, a fundamentalist from the Calvary Baptist Church in Conroe. "The Republican Party of Texas now has God on its side. Some people made us out to be barbaric or something, but really the change from the Republican mainstream to us is not all that great."

The most passionate of the fundamentalist issues in Texas this year, the one that turned many evangelicals into party activists, is state regulation of church and home schools. Jim Mattox, the Democratic attorney general, has taken on the fundamentalists by strictly enforcing a law requiring all schools to be licensed by the state and to meet certain basic standards. Mattox has fined Fort Worth pastor W.N. Otwell's Community Baptist Church and Boys' Home for refusing to be licensed, and is threatening to sell the school property if Otwell does not adhere to the state requirements.

Clements has supported the fundamentalists on this issue, saying he will not interfere in the church and home schools if he is elected governor. But it is not an issue with which all state Republicans feel comfortable.

"I attended an evangelical church school, North Side Baptist Academy, and I must say now that I think the state should regulate them," said Karen Beane, a delegate from Houston. "I know places where sixth-grade biology is being taught to 11th-graders. These people say they don't want government telling them what to do, then they try to tell everyone else what is wrong or right."

Beane's husband, Del. David Beane, said he was "shocked" by resolutions that were passed at his district caucus, including one that opposed abortion even in cases where the mother's life was threatened because "it was God's will." Said Beane: "It was unbelievable. I don't think this is where the party should be heading if it wants to be the majority party."