Gatlin Brothers

The Gatlin Brothers — Steve (from left), Larry and Rudy — bring Larry’s deep catalog of country hits to the Waco Hippodrome on Thursday.

Rudy Gatlin, the youngest of the three Gatlin Brothers, has a simple explanation for how three Texas brothers have enjoyed sustained success over four decades in country music: “Larry wrote some great songs. We sing in tune and we sing harmony,” he said in a recent phone interview.

There’s more to the Gatlin Brothers’ long career than that, of course, but Rudy’s summation shows his belief in the staying power of a song. For most of their 43 years as a performing group, the Gatlins have had the songs, thanks in large part to Larry, the oldest Gatlin to middle brother Steve and Rudy.

Larry ranks fourth among BMI songwriters in the number of Top 40 hits written, seven of which topped country charts, with one Grammy Award for “Broken Lady” and an Academy of Country Music award for “All The Gold in California.” “Houston (Means I’m One Day Closer to You)” made Billboard’s list of Greatest of All Time Top Country Hits.

The Gatlin Brothers come to the Waco Hippodrome on Thursday for a concert that sticks to the essentials: Larry, 71, and Rudy, 65, on guitar and Steve, 67, on bass, lots of Gatlin hits and some they thought should have been. “We stick to the basic show we’ve been doing for a while and throw in a couple of misses,” Rudy said.

The Gatlins grew up in West Texas, including Odessa and Abilene — their father was an oilfield worker — and singing in the church from their earliest years. After graduating from the University of Houston, Larry joined the gospel group The Imperials. Country star Dottie West met him at a Las Vegas concert and persuaded him to try his hand in country music.

In Nashville, his songwriting and singing found champions in Kris Kristofferson and Johnny Cash. As a solo performer, Larry scored his first major hit with the Grammy Award-winning “Broken Lady” and by the mid-1970s, Steve and Rudy were in Nashville, too, singing backup for Tammy Wynette. In 1976, the brothers started performing together professionally, and Larry Gatlin and the Gatlin Brothers became country music fixtures in the late 1970s and 1980s.

In addition to extensive touring, the Gatlins sang frequently on television and at high-profile occasions such as the World Series, the National Basketball Association championships and presidential appearances. The trio also had their own variety show on television, the ABC special “Larry Gatlin and the Gatlin Brothers.”

The brothers stopped touring together in 1994, focusing on their theater in Myrtle Beach, South Carolina, and individual careers. Both Larry and Rudy did stints in theater, Larry with the Broadway production of “The Will Rogers Follies” and his own musical “Quanah” while Rudy appeared in revivals of “Oklahoma!” and “Annie Get Your Gun.”

The Gatlin Brothers returned to performing together in the early 2000s and fans have flocked to their shows. Rudy attributes that to the solid work of producer Fred Foster of Monument Records in the Gatlins’ heyday. “Those records sound differently than the ones today . . . but they stand the test of time,” he said. “You cut ’em and record ’em and do the best you can with what you have at the time, but, by and large, they’re pretty incredible records.”

The Gatlins also aren’t done yet, releasing “The Gospel According to Gatlin” in 2015, making regular appearances on the “Grand Ole Opry” and contemplating a new album of duets and collaborations with other country performers. “We’ve been wanting to do it a long time,” Rudy said.

At the Hippodrome on Thursday, however, it’s all about entertaining the audience in front of you. “We’re still happy and proud and grateful to do it,” said the youngest brother. “We don’t take that for granted.”