The first round of results from Nevada are finally in. Adam Laxalt, the Trump-endorsed candidate for Senate, has a comfortable early lead. If he wins, he will face Catherine Cortez-Masto, one of the most vulnerable Democratic senators, this fall.

Mayra Flores, a Republican, has won the special election in Texas to replace former Representative Filemon Vela in a Hispanic-majority district in the Rio Grande Valley. Flores will be the first Republican from the district and the first Latina Republican from Texas in Congress.

With just over 25 percent of precincts reporting, it’s looking like a steeper hill to climb for Tom Rice to make it to a runoff. He’s trailing his primary challenger Russell Fry by 20 points. Fry has 45 percent of the vote.

Gov. Janet T. Mills of Maine, a Democrat, and Paul LePage, a Republican, advanced to the general election for governor. Both were uncontested. LePage was governor from 2011 to 2019, when he was succeeded by Mills.

Early returns from Charleston County look good for Representative Nancy Mace, the Republican competing with a Trump-endorsed challenger, Katie Arrington. But no results are in from Beaufort County on the state’s south coast — Arrington’s stronghold.

In the Rio Grande Valley of Texas, voters are casting ballots in a special election to replace Representative Filemon Vela, a Democrat. Republicans are aggressively courting voters in the heavily Hispanic district, but the winner will only hold office until January.

In Nevada’s sprawling Fourth Congressional District, Republicans are vying to take on Representative Steven Horsford. One of the top G.O.P. candidates, Sam Peters, has the backing of some of the most far-right Republicans in the House, like Representatives Andy Biggs and Paul Gosar of Arizona.