More than a year before the 1984 presidential election, no one has captured the hearts and minds of Hispanic voters in the Southwest. But both political parties are trying.

Democrats are striving to bring Hispanics back into their traditional role as reliable party loyalists.

President Reagan, beginning with a campaign swing through the Southwest this weekend, is striving to erode that traditional Democratic support further, as he sucessfully did in 1980.

It is a volatile contest that neither side can afford to lose but which neither has won. As the nation's second-largest and fastest-growing minority, Hispanics are certain to play a pivotal role in the big-state strategies of both Reagan and his Democratic challenger next year.

To counter an expected high black turnout for Democrats next year, Reagan's political strategists are again turning to Hispanics. But Reagan faces new problems this time that could make it far more difficult.

Today Reagan gave 42 Hispanics in his administration a pep talk at the White House, citing the Hispanics he has appointed and pledging to "continue to reach out to the Hispanic community for their ideas."

This weekend, at the outset of a series of campaign events targeted at Mexican Americans, Reagan is to address the American G.I. Forum, a Hispanic veterans' group meeting in El Paso, and travel to La Paz, Mexico, to meet President Miguel de la Madrid. He also is to visit Tampa, where he is to address a Cuban American audience.

His trip comes on the heels of a conference here of Hispanic activists who are launching a drive to register 1 million new Hispanic voters next year, most of whom presumably would vote for a Democrat.

The struggle is now focused on Mexican Americans, who make up about 60 percent of the nation's Hispanics and are concentrated in the southwestern states, including the electoral prizes of California and Texas.

Cuban Americans in Florida have long been strong Reagan supporters. One of the most rousing receptions Reagan has received was from Miami's huge Hispanic community, where he assailed Cuban President Fidel Castro.

Puerto Ricans, mostly in New York, tend to back Democrats.

Going back to the days of the "Viva Kennedy" campaign of 1960, Mexican Americans also traditionally have voted for Democrats. But Reagan did better among them in 1980 than had any GOP presidential candidate since World War II, winning between 25 and 30 percent of their votes.

Of the 14.6 million Americans who identified themselves as Hispanic in the 1980 census, about 5.5 million were citizens eligible to vote. Officials agree that only 3.4 million did so, however.

Democrats say they believe Reagan was as successful with Hispanics as he was in 1980 because they failed to mount a voter registration and turnout effort. Ann Lewis, political director of the Democratic National Committee, said 1980 "represented a fluke, if you will."

"We've got to get the vote out. We didn't do it" in 1980, she said.

Even if the voters get to the polls, however, Democrats may have another stumbling block, which was indirectly evident in the ballroom of San Antonio's Gunter Hotel one night this week.

The one possible Democratic presidential candidate who probably could turn out Hispanic voters and deny Reagan his 1980 share had his audience on its feet, cheering his attacks on Reagan.

But Sen. Edward M. Kennedy (D-Mass.) is not running for president. And out in the hallway, while Kennedy was speaking, one organizer of the voter registration conference observed, "The Republicans are going to be hard to beat next year."

In a straw poll of the mostly Democratic activists at the conference, former vice president Walter F. Mondale was the first choice with 44 percent. Sen. John Glenn (D-Ohio) was second with 20 percent.

Mondale may be in tune with many of the Hispanic political leaders and activists, but there are lingering doubts about his electibility, and Glenn seems a distant figure to many Hispanic leaders interviewed here.

Republicans often have claimed an affinity with Hispanic voters on the basis of shared conservative views on social issues, such as opposition to abortion. Reagan has demonstrated, both in his California campaigns and in the 1980 race, that he can appeal to Hispanics by emphasizing that he shares with them family-oriented, traditional values.

"It's this administration which shares the Hispanic values of family, neighborhood, church, freedom and opportunity," Vice President Bush told the voter registration group this week, borrowing a phrase that aides expect Reagan to use often between now and election day.

In his 1980 campaign, Reagan's litany of shared values also included "work," but high unemployment has become one of his most serious liabilities in the Hispanic community. Education also remains a high-profile issue, as polls done for the White House have shown.

The most striking evidence of this shift in sentiment--one that worries many Republicans--was the high Hispanic and black voter turnout in Texas against Republican Gov. Bill Clements last year.

Clements had made many gestures to the Hispanic community during his term and in his campaign, but won only about 17 percent of the Mexican American vote. The turnout against him among Hispanics was particularly high in south Texas, where joblessness had soared.

The campaign rhetoric aimed at Hispanics this week suggested that the so-called "fairness issues"--Reagan budget cuts in social programs for the poor, joblessness, civil rights--remain a potent weapon that Democrats intend to exploit among Hispanic voters against Reagan.

Kennedy declared to applause that "Ronald Reagan must love poor people because he is creating so many of them." New Mexico Gov. Toney Anaya said Reagan has installed "a scheme of greed and benign neglect papered over with personal charm."

One question is how Mexican Americans will react to Reagan's military show of force in Central America. Democratic political leaders, such as San Antonio Mayor Henry Cisneros, have staked out their opposition to administration efforts to increase the American military presence in the region, and some predict that the highly respected Cisneros will sway grass-roots opinion in Mexican American communities against the Reagan approach.