What to Watch in Primaries in Maine, South Carolina, Nevada and North Dakota

A special House election will also be held in Ohio to replace a retiring Republican congressman.

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Maine Republicans will choose from two candidates who are vying to give Representative Jared Golden, a Democrat, another tough re-election contest.

The presidential primary season is over, but down-ballot primaries are still happening across the country. Candidates will be on the ballot on Tuesday in five states: South Carolina, Nevada, Maine, North Dakota and Ohio, where a special House race will take place.

Representative Bill Johnson retired from Ohio’s Sixth Congressional District in January, and State Senator Michael Rulli, the Republican nominee for the seat, will face off against Michael L. Kripchak, the Democratic nominee. Former President Donald J. Trump won that district in 2020 by a margin of 29 percentage points.

Here are the primaries to keep an eye on:

Nancy Mace, a Trump vice-presidential contender, will be on the ballot in South Carolina.

Representative Nancy Mace, Republican of South Carolina, who is a contender to be Mr. Trump’s running mate, faces a primary opponent backed by former Speaker Kevin McCarthy, who opposes her because she voted to oust him from the speakership last year. The primary, in the state’s First Congressional District, comes just days after the House Ethics Committee started looking into Ms. Mace’s use of a congressional reimbursement program.

Catherine Templeton, Ms. Mace’s opponent, worked for Nikki Haley when she was governor of South Carolina, and Ms. Templeton ran for that office in 2018. Ms. Mace was once a moderate ally of Ms. Haley’s, but she shifted to the MAGA wing of the Republican Party when her district was redrawn in 2022, making it more conservative.

The Third and Fourth Congressional Districts will also host competitive Republican primaries. Representative Jeff Duncan retired from his seat in the deeply conservative Third District, and, in the Fourth District, Representative William R. Timmons IV, who fended off Republican challengers in the 2022 primary, will be challenged by State Representative Adam Morgan, the leader of what is their chamber’s version of the hard-right Freedom Caucus.

The leading Republican Senate candidate in Nevada has a last-minute endorsement from Trump.

Nevada Republicans will choose their nominee for a U.S. Senate seat from a crowded field.

The leading candidate, Sam Brown, a former Army captain, received a last-minute boost in the form of an endorsement from Mr. Trump, who weighed in on the race on Sunday night, though after early voting had ended.

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