CAPE CANAVERAL, Fla.--Elon Musk’s space company had just pulled off a momentous feat: landing the first stage of a rocket on a landing pad at the Air Force Station here Monday. And Jeff Bezos was among the first to offer congratulations on twitter.

“Welcome to the club!”

It was a backhanded compliment in an ongoing rivalry between two billionaires who are now engaged in their own space race.

Last month, Bezos’s Blue Origin launched a rocket just past the boundary of space, and then landed it vertically in rural West Texas. That was celebrated as a historic achievement since no rocket had ever traveled that far before coming back to land.

Being able to reuse rockets was the “Holy Grail” of space flight, Bezos said, an accomplishment that would dramatically lower the cost since rocket boosters are usually discarded in the sea after one use. (Bezos owns The Washington Post.)

Triumphant, Bezos tweeted a photo of the recovered first stage, calling it the “rarest of beasts—a used rocket.”

“Not quite ‘rarest,’” Musk tweeted back, pointing out that SpaceX has previously launched test rockets a few hundred feet into the air and landed them.

In a series of tweets, he continued to needle Bezos, saying that what SpaceX was now attempting—landing a much larger and more powerful rocket capable of sending a payload into orbit—was a far more difficult feat that the landing of Bezos’ suborbital rocket.

Bezos, in his tweet Monday, couldn't resist noting the landing involved a "suborbital" booster stage.

The pair, both billionaires with the goal of opening up space to the masses, have clashed repeatedly over the years. A few years ago, when SpaceX and Blue Origin were both bidding to take over historic launch pad 39A at the Kennedy Space Center. SpaceX won the lease, and Blue Origin protested to the Government Accountability Office, but lost, and Musk rubbed it in.

“If they do somehow show up in the next 5 years with a vehicle qualified to NASA’s human rating standards that can dock with the Space Station, which is what 39A is meant to do, we will gladly accommodate their needs,” Musk wrote in an email published at SpaceNews.com. “Frankly, I think we are more likely to discover unicorns dancing in the flame duct.”

And earlier this year, Blue Origin announced it would also occupy some prime real estate at Cape Canaveral, Launch Complex 36, which is just down the road from pad 39A, making the pair neighbors.

The two companies have also squabbled over landings. Blue Origin had a patent that gave it the right to launch and then land rockets on a floating barge at sea. Musk challenged it, saying that the idea of a sea landing had been around for years. And his company even attempted it—twice failing earlier this year.

Now SpaceX also has Landing Zone 1, a massive landing site on the Cape, where on Tuesday, SpaceX rocket booster was still standing, visible from Bezos’ new launch site.