You see, Musk's Starlink and Bezos' Project Kuiper are both being evaluated by federal regulators, and have become involved in a public disagreement over their respective satellite ventures.
Musk, who is the CEO of both Tesla and SpaceX, took to Twitter to accuse Amazon supremo Bezos of trying to 'hamstring' his Starlink project and also aimed a barb at him suggesting that Project Kuiper is 'at best several years away' from taking off.
Then, Bezos - who doesn't tend to air out his dirty laundry on his own Twitter - said through Amazon that it was in fact Musk who is doing the hamstringing - if that's a word - and attempting to 'smother competition in the cradle'.
He also said that Starlink is creating a 'dangerous environment for collisions' in orbit above earth.
This is because Musk is asking the Federal Communications Commission to allow for some Starlink satellites to operate at lower altitudes that it had originally set out for.
Amazon aren't happy with this, as they believe it would interfere with other satellites - most notably the Project Kuiper ones - that they plan to send into low-earth orbit.
This is far from the first time the two multi-billionaires have faced off with each other over their respective plans in space.
Both have ambitions of sending tourists into space, and Musk has even branded Bezos a 'copycat' because of Amazon's plans, whereas Bezos has openly mocked Musk's lofty goal of sending humans to Mars.
Whilst they battle it out for supremacy of the stars, they are also locked in a battle over their own wealth, and have interchanged positions as the world's richest person.
Musk briefly assumed the top spot earlier this year, but Bezos quickly moved past him once again.
On Tuesday, Musk tweeted: "It does not serve the public to hamstring Starlink today for an Amazon satellite system that is at best several years away from operation."
In a presentation by SpaceX Director of Satellite Policy David Goldman, the company also accused Amazon of trying to 'stifle competition' - a claim that Amazon rejected in a statement.
They wrote: "The facts are simple. We designed the Kuiper System to avoid interference with Starlink, and now SpaceX wants to change the design of its system.
"Those changes not only create a more dangerous environment for collisions in space, but they also increase radio interference for customers.
"Despite what SpaceX posts on Twitter, it is SpaceX's proposed changes that would hamstring competition among satellite systems. It is clearly in SpaceX's interest to smother competition in the cradle if they can, but it is certainly not in the public's interest."
Starlink is aimed at creating a global high-speed internet system using 12,000 satellites in orbit around the earth.
So far, they've got more than 1,000 up there already.
Project Kuiper has yet to launch any satellites, but plans to send 3,236 up to rival Musk's Starlink.
Meanwhile, space experts have warned that sending too much 'space junk' into orbit around the earth could lead to collisions with spacecraft or the International Space Station, disrupt radio frequencies, or even block out the stars.