_{Editor’s note: This story has been updated throughout.}

Two new Republicans are poised to claim seats in the Texas Senate: Travis County eye surgeon Dawn Buckingham and state Rep. Bryan Hughes, R-Mineola.

On Tuesday, Buckingham won the Republican runoff for the outgoing seat of state Sen. Troy Fraser, R-Horseshoe Bay, in Senate District 24. Buckingham finished the night with 26,413 votes, 61 percent of the total count, according to complete but unofficial returns. That’s compared to 16,645 votes, or 39 percent, who backed state Rep. Susan King, R-Abilene.

Buckingham will face Democrat Jennie Lou Leeder in the Nov. 8 general election. The rural-suburban hybrid district spans roughly 20,000 square miles, from the northwest suburbs of Austin up to Abilene, and is considered safely Republican.

“It has been an honor traveling across the most beautiful part of Texas and meeting so many fantastic people,” Buckingham said in a prepared statement. “I look forward to being the conservative voice at the Capitol!” 

In another highly anticipated Republican Senate primary, Hughes on Tuesday won the runoff for Senate District 1, all but guaranteeing he will win the seat of outgoing state Sen. Kevin Eltife, R-Tyler, in the Texas Senate.

Hughes ended his night earning 27,348, 69 percent of the total count. That’s compared to 12,105 votes, or 31 percent, for his opponent, state Rep. David Simpson, R-Longview.

Hughes will not face a Democratic opponent in November’s general election.

In the low-turnout election, Hughes and Buckingham both coasted to double-digit victories after running campaigns to the right of their opponents.

Hughes scored a late endorsement from U.S. Sen. Ted Cruz in addition to previous endorsements from some of the state’s top Republican leaders, including Lt. Gov. Dan Patrick, Attorney General Ken Paxton and former Gov. Rick Perry.

Buckingham also claimed an endorsement from Perry, in addition to nods from Tea Party stalwart and state Rep. Jonathan Stickland, R-Bedford, and fellow doctor and state Sen. Charles Schwertner, R-Georgetown.

Julian Aguilar contributed to this report.