Republican presidential hopefuls faced off in sleepy Nevada caucuses and a hard-fought South Carolina primary today, a pair of contests likely to winnow an unwieldy field of rivals.

Democrats shared the stage in Nevada, with Senators Clinton and Obama vying for a victory and the campaign momentum that goes with it.

Alone among the Republican contenders, Rep. Ron Paul of Texas aired television ads in Nevada, and the libertarian-leaning Texan looked for his best showing of the campaign season. A former Massachusetts governor, Mitt Romney, campaigned in the state, hoping to add to his earlier victories in the Wyoming caucuses as well as last Tuesday’s Michigan primary.

Nevada offered more delegates but far less appeal to the Republican candidates than South Carolina, a primary that has gone to the party’s eventual nominee every four years since 1980.

That made it a magnet for a former Tennessee senator, Fred Thompson, who staked his candidacy on a strong showing, as well as for Mr. Romney, Senator McCain, and a former Arkansas governor, Michael Huckabee.

Mr. McCain, a former Vietnam prisoner of war, appealed to a large population of military veterans in South Carolina, and stressed his determination to rein in federal spending as he worked to avenge a bitter defeat in the 2000 primary.

Mr. Huckabee reached out to evangelical Christian voters, hoping to rebound from a string of disappointing showings since his victory in the January 3 Iowa caucuses.

Mr. Romney campaigned on a pledge to help restore the state’s economy, much as he did in winning the Michigan primary earlier in the week.

Alone among the major Republican contenders, Mayor Giuliani skipped the day’s events. He camped out in Florida, the first of the big states to vote, with a winner-take-all primary on January 29.

A wild card in the South Carolina race was the wintry weather. In northern areas of the state, snow was forecast and expected to intensify through the day, with accumulations reaching 3 inches. Any snow tends to bring South Carolina to a slow crawl at best. The state has little snow removal equipment and during a recent light snowfall, some schools closed or delayed opening before the first flakes fell.

Bad weather and some last-minute push polling could put a damper on turnout for the primary, with first-time voters, senior citizens, independents and those still wavering staying home, according to political experts.

“It’s not going to deter the party activists who will vote come fire or hail storm or 4 inches of snow,” a University of South Carolina political scientist, Blease Graham, said.

If the Republican race had no clear front-runner, the Democrats had two, and little room in the campaign spotlight for the third man on the ballot, a former senator, John Edwards.

Mr. Obama and Mrs. Clinton both ran all-out in Nevada, even though only 25 delegates are at stake.

Mr. Obama won the backing of an influential Culinary Workers Union. That, in turn, led to an unsuccessful lawsuit by some of Mrs. Clinton’s supporters who hoped to ban specially arranged caucuses along the Las Vegas Strip that could draw thousands of unionized casino and hotel workers.

Mr. Obama, hoping to become the first black president, spent nearly $1 million in television commercials. Mrs. Clinton, campaigning to become the country’s first woman chief executive, ran nearly $700,000 worth of commercials, and a union group backed her with nearly $100,000 on an independent ad campaign.

President Clinton was a constant presence, as well, in a state he carried twice on his own in 1992 and 1996.

Remarkably, neither Mr. Obama nor Mrs. Clinton has aired a television commercial criticizing the other, and both of the rivals stepped back earlier in the week from a controversy over race. But that didn’t prevent almost constant sniping between the two camps, each pointing out alleged inconsistencies in the other’s record.