The servicemen say their health was damaged by radiation from nuclear weapons testing in the 1950s.
It took place in Australia, on Christmas Island and in the Pacific Ocean between 1952 and 1958. They say they've suffered cancer, skin defects and fertility problems as a result.
The veterans have been fighting to be allowed to ask for compensation for about two years. Today at the Supreme Court they were told they can't seek damages from the Ministry of Defence over the testing. An earlier legal ruling means some of them will be able to proceed with the claims.
The Ministry of Defence has acknowledged "a debt of gratitude", but denies negligence.
A spokesman said :