The 40-year-old billionaire twins Tyler and Cameron Winklevoss have been on the road with their rock band, Mars Junction, since early last month, crisscrossing the country to offer their versions of songs by Blink-182, the Red Hot Chili Peppers, the Police, Pearl Jam and Journey. Tyler sings; Cameron plays guitar. On Saturday, they rolled into Amagansett, N.Y., the Long Island beach town not far from where they spent their childhood summers.

They arrived in grand style, cruising down Main Street in a 45-foot Prevost tour bus with “Mars Junction” in huge lettering on the side. A Mercedes-Benz Sprinter brought up the rear. The twins’ retinue included the four musicians in the band, a documentary filmmaker, a merchandise salesman and assorted staff members.

The two vehicles parked in front of the Stephen Talkhouse, a venue with an old-salt vibe where a number of marquee performers have taken the stage over the decades, including Jimmy Buffett, Jimmy Cliff, Billy Joel, Paul McCartney, Paul Simon, Sheila E. and Suzanne Vega. Mars Junction was closing out the tour with two nights at the Talkhouse on Saturday and Sunday. Tickets were $50.

The twins, whose cryptocurrency company, Gemini, laid off 10 percent of its staff in the recent crypto crash, hit a bump on the road to Amagansett. An audience member at the band’s show at the Wonder Bar in Asbury Park, N.J., posted a video of Tyler trying and failing to match the crystalline high notes of the singer Steve Perry in Mars Junction’s rendition of Journey’s 1981 hit “Don’t Stop Believin’.” The clip went viral, and the comments on social media about the twins — former Olympic rowers who made a fortune in Bitcoin after having a role in the creation of Facebook — came in hot.

Tyler and Cameron Winklevoss, who were born in nearby Southampton and grew up in Greenwich, Conn., had a much warmer reception at the Talkhouse. By 7 p.m. on Saturday, the place was packed, mainly with young adults in Bermuda shorts and summer dresses who appeared to belong to the same crowd as the Harvard-educated twins. Their parents, Carol and Howard Winklevoss, were in attendance, as were several family friends.

The twins took the stage and dove into their opener, “Top Gun Anthem,” the instrumental theme to the 1986 film and its recent sequel. With his mustache, slicked-back hair, aviator shades and wallet chain hanging from a back pocket, Tyler had a look somewhere between “Top Gun” and Tommy Bahama. Cameron, in an orange shirt and white slacks, had more of a surfer vibe.

Suddenly, his legs wide apart and the microphone held sideways, Tyler led the band into Rage Against the Machine’s “Killing in the Name.” “Now you do what they told ya!” he sang before leaping into the crowd, where he engaged in a flurry of high-fives and fist bumps with the Mars Junction faithful.

“What up, Talkhouse!” he said after the song was done. “Fourth of July weekend, it’s the big one! Ready to rock, you guys?”

The hits kept on coming: Kings of Leon’s “Sex on Fire”; Mumford & Sons’ “The Wolf”; the Red Hot Chili Peppers’ “Can’t Stop.” When Tyler sang Sublime’s “Santeria,” he made a change to the line “Well, I had a million dollars” by replacing the word “million” with “billion.” Cameron executed a wah-wah guitar solo and took a swig of Liquid Death water.

Then came the challenging part of the show: the Police medley, which required Tyler to hit the high notes so effortlessly sung by a youthful Sting in his 1980s glory.

“So Lonely” segued into “Message in a Bottle,” which morphed into the hard-rocking “Synchronicity II” (“The factory belches filth into the sky!” Tyler sang) before settling into the reggae vibe of “Walking on the Moon.” Tyler was stretching his voice to the limit. Why not make it easier on himself by starting it off in a lower key? But that is not the Winklevoss way.

The crowd sang along with the next one, “Flagpole Sitta,” a 1997 hit for Harvey Danger. When the music died down, a young man in the audience repeatedly screamed out a profane chant against Mark Zuckerberg, whom the Winklevoss twins sued unsuccessfully, accusing him of denying them their fair share of Facebook money.

“I don’t know what you’re saying,” Tyler said to the rowdy fan, the hint of a smile on his face.

He got nostalgic in his introduction to Pearl Jam’s “Even Flow.”

“Let’s go early ’90s, yeah?” Tyler said to the crowd. “What do you think? Early ’90s? Pre-internet? Can you handle that? No social media? All right, you want to go back there?”

He channeled Eddie Vedder’s growl. Cameron busted out two solos.

“Whooooooo!” said the crowd.

“We’re going to stay early ’90s for this next one,” Tyler said. “Ready for some Nirvana?”

The crowd whooped again.

“OK, that feels like a yes!”

Then came “Smells Like Teen Spirit.” As they played the next song, the Red Hot Chili Peppers’ “Suck My Kiss,” their mother, Carol, was clapping along to the beat as their father, wearing a blue blazer and button-down shirt, maintained a stoic demeanor.

For the song “You’re So Last Summer,” by Taking Back Sunday, Cameron put on a Mars Junction cap. More were available at the merch table for $20.02 apiece.

After the audience sang along to “Mr. Brightside” by the Killers, Mars Junction offered a pair of Journey songs as encores: “Don’t Stop Believin’” and “Any Way You Want It.” The lights came up to the sound of AC/DC’s “Hell’s Bells” on the Talkhouse sound system. The twins left to have a late dinner with their parents at Gurney’s in Montauk.

Before the Sunday evening show, the brothers took a moment to chat in an upstairs room at the Talkhouse. As Tyler cracked open a Liquid Death, he said the previous night’s show had the feel of a homecoming and noted that his parents still had the beach house in nearby Quogue. He added that Mars Junction was in a somewhat vulnerable position, since it plays such familiar songs.

“When you play covers, you’re judged against the recording,” Tyler said. “And the more iconic the song, the more people know the recording, and live’s a little different. So it’s a tough thing.”

One thing the Mars Junction experience has taught them, the twins said, was that the life of a touring musician can be wearying.

“You’ve got to rest for these shows,” Tyler said. “It’s a huge exertion and, as a vocalist, your voice can go if you’re not careful.”

“Guitars don’t get tired,” Cameron said. “But humans do.”