Charlie and his brother Spike have become an internet hit.
A video showing them stumbling around the floor before keeling over in apparent paralysis has already notched up almost a million viewings.
But the reason behind their internet fame has already claimed Spike's life, and continues to be a source of puzzlement for vets treating Charlie.
Their condition, suspected to be myotonia congenita, also known as "fainting goat" syndrome, is a disorder that affects the muscles used for movement.
It is extremely rare in cats - Charlie and Spike are the only known cases in the UK, according to the Royal Veterinary College. There have been six reported cases outside the UK, two from the US and four from New Zealand.
The cats' owner Edward Scarr said he realised there was a problem soon after taking Charlie home.
"I noticed that he was having trouble standing up properly and that something wasn't right," he said. "He would be walking around and then at the slightest sound collapse into a rigid paralysis for a while before returning to normal.
"When I took him back to the pet shop I was told that Charlie's brother had been returned with the same condition, and that he was going to be put down. I ended up taking both cats home."
Edward took the cats to the Royal Veterinary College three weeks ago.
He said: "Sadly Spike has since died. His condition was more extreme and it affected his respiratory system.
"Charlie is now going to be treated with drugs that have never been used on cats before.
"I don't think he'll ever be an outside cat. He can't jump or pounce. If he's lying still he seems to be ok but he has problems if he hasn't been on his feet for a while.
"After a few minutes he'll take a few tentative steps down the corridor. He's a very sweet little boy."
Holger Volk, head of veterinary neurology and neurosurgery at the Royal Veterinary College, said: "We saw that when Charlie was startled by a loud noise, or if he got his claws caught in something, he would become stiff and fall over. These seemed to be stress moments for him.
"He contracts his muscles but the relaxation of the muscles is delayed which causes the rigidity.
"The clinical appearance of the episodes resembles the one seen in goats with myotonia congenita. It is most likely a gene defect and we are trying to establish whether it is the same as that in the so-called "fainting" goats.
Dr Volk said he hoped to have more information following the post mortem on Spike.
"Charlie is being put on a long-term course of drugs which will stabilise the membrane of the muscles so they won't contract as much," he said.
"The main issue is to keep the cat as calm as possible and remove any sudden stress moments which cause the muscles to contract."