The Privy Council has rejected the appeal of six Pitcairn Islanders against their convictions two years ago for incest and the rape and indecent assault of girls as young as ten.
The judges rejected the mens' argument that they were not British subjects, that English law did not apply on Pitcairn and that if it did, the population was unaware of the fact.
The men argued that an order in 1970 making fresh provision for English law on the island was invalid because Pitcairn was never a British possession.
However, the judges ruled Pitcairn was run by the crown as a British possession for more than a hundred years and it would be unthinkable for the court to reject a law affirming it as part of crown terrirty.
The judges also said there was no doubt that laws on sexual offending applied to the islanders.
The men will now serve out their sentences on the island.
