Equipment failure is blamed for killing the sharks
The Sandbar sharks appeared to have been poisoned by excessive ozone in their tank at the National Marine Aquarium in Plymouth.
Three of the sharks died on Monday, the fourth between Monday evening and Tuesday morning.
Seven others were being monitored by staff who had spent hours in the water, trying to keep them alive.
Sand Tiger, Nurse and Bambo Cat sharks which were also in the tank are said to be unaffected.
The Sandbar sharks, each worth £7,000, had been brought to Plymouth to replace a previous batch that died soon after arriving in 1998.
They were killed by hypothermia after their flight from Florida was delayed by a snowstorm at Amsterdam.
The latest deaths were blamed on a malfunction in equipment that should have controlled ozone levels in the tank.
Aquarium spokesman Kelvin Boot said the meter was reading zero and kept asking for more ozone.
"Whenever you get that sort of failure it is pretty gutting," he said.
'Bad luck'
"Their swimming pattern wasn't quite right and straight away the people who look after them could tell there was something wrong.
"All the fail-safe systems in the world don't seem to be able to prevent this happening.
"It is just bad luck and appears to have been unavoidable."
He said staff had struggled to prevent the deaths.
"They spent hours and hours in the water trying to keep them alive."
The aquarium has launched a full inquiry into the failure of the equipment.
A spokesman for the Shark Trust, Clive James, said: "I think it is a tragic accident.
"The Shark Trust does recognise there is a real value to have the fish in aquaria.
"We know the people here in the aquarium take great care at the highest levels of animal husbandry."
Ethical problems
When the first batch of sharks died, the animal welfare charity Zoocheck criticised the aquarium.
Spokesman Dave Spratt had said: "There is no justification that we can see at all for bringing sharks to Plymouth.
"There is no educational value. There is no conservation value."
The RSPCA has said it will not prosecute because the deaths were an accident.
But it also said the incident "underlines the practical and ethical problems of keeping sharks in captivity".