Republican Sen. Richard Shelby beat back four Republican challengers to clinch his party’s nod in Alabama with 65 percent of the vote, easily surviving the threat of an upset in the anti-establishment year of Donald Trump.

Elsewhere in the state, GOP incumbent Reps. Martha Roby and Bradley Byrne won their own intraparty contests, avoiding contentious runoff races that could have impeded their focus on the general election. Roby won with 66 percent of the vote in a three-person race. Byrne defeated challenger Don Young with 60 percent of the vote in a rematch of the 2013 special election race that sent Byrne to Congress.

In Texas, House Ways and Means Committee Chairman Kevin Brady (R) narrowly avoided a run-off with 53.3 percent of the vote. Fellow Texan House Rules Committee Chairman Pete Sessions (R) enjoyed a wide victory with more than 61 percent of the vote despite early concerns that Trump voters would support one of several anti-establishment challengers.

The congressional results suggest that Trump’s appeal may not be directly linked to the fate of House and Senate Republicans, whose primary season is just starting to kick into high gear. Trump, who is running a wildly unconventional campaign to “Make America Great Again,” swept most of the Super Tuesday nominating contests, including Alabama — although Sen. Ted Cruz (R) won his home state of Texas.

Some Republican strategists fear that Trump’s success could turn previously noncompetitive  primary races into heated battles for survival for House members and senators.

“My general advice to incumbents is don’t be scared,” said GOP strategist and former National Republican Congressional Committee deputy political director Brian O. Walsh. “Be prepared and go run the campaign you need to run.”

Shelby was first elected to the Senate in 1986 and chairs the Banking Committee. He previously chaired the Senate Intelligence Committee and represented Alabama’s 7th congressional district from 1979 to 1987. Shelby faced four challengers: Jonathan McConnell, Marcus Browman, John Martin and Shadrack McGill.

McConnell, considered Shelby’s strongest competitor, is 33 and a relative unknown in the state. He attacked Shelby for his “big spending ways.” Shelby was backed by the NRA, the Tea Party Patriots Citizens Fund, National Right to Life and many other groups. He is also supported by fellow Alabama Republican Sen. Jeff Sessions, who recently announced his endorsement of Trump.

Brady, who has represented Texas’ 8th district since 1997, faced off against former Texas state Rep. Steve Toth (R), who was favored by several local tea-party affiliated groups.

Sessions, who represents Texas’ 32nd district, ran against oil and gas executive Russ Ramsland. Ramsland accused Sessions of becoming more moderate since he took office in 1997.

Primary challenges have recently posed a greater danger than general elections to some Republican incumbents following the rise of the tea party. But campaign strategists said the concern is particularly acute this year as the anti-establishment climate is inspiring voters who would normally stay home to come out and vote in the year of Trump.

The security blanket once provided to incumbents by broad name recognition and financial help from party backers is fraying, leaving lawmakers to wrestle with how much to embrace their congressional experience while seeking to assure restless primary voters  that they share their anger over the status quo.

Walsh said that the biggest mistake incumbents make is not taking their primary challengers seriously. Many strategists point to former House Majority Leader Eric Cantor (R-Va.), who lost his seat in 2014 to a shockingly strong primary challenge from tea party favorite David Brat. A similar story played out in 2010 when Mike Lee ousted Robert F. Bennett (R-Utah), who had been in the Senate since 1993.

Lawmakers will have to campaign hard to survive runoffs — but those elections typically favor incumbents more than statewide primaries where presidential candidates and their personalities drive the day.

“When you talking about a presidential turnout you’re talking about a lot of less frequent voters who just are less involved,” Walsh said.