From BBC News:
A study in Nature magazine suggests the species may have lived in Gorham’s Cave on Gibraltar up to 24,000 years ago. The Neanderthal people were believed to have died out about 35,000 years ago, at a time when modern humans were advancing across the continent. The new evidence suggests they held on in Europe’s deep south long after the arrival of Homo sapiens. The research team believes the Gibraltar Neanderthals may even have been the very last of their kind.
Though once thought to have been our ancestors, the Neanderthals are now considered an evolutionary dead end. They appear in the fossil record around 230,000 years ago and, at their peak, these squat, physically powerful hunters dominated a wide range, spanning Britain and Iberia in the west to Israel in the south and Uzbekistan in the east. Our own species, Homo sapiens, evolved in Africa, and displaced the Neanderthals after entering Europe about 40,000 years ago.
More here.