Researchers from across Europe found that humans' ancestors exchanged ideas and culture as well as competed for food.
"I think we can set aside the idea of a rapid extinction of Neanderthals caused solely by the arrival of modern humans. Instead we can see a more complex process in which there is a much longer overlap between the two populations where there could have been exchanges of ideas and culture," said Professor Thomas Higham.
Researchers formerly thought humans and Neanderthals only co-existed on Earth for about 500 years.
"They were hunting the same animals, collecting the same plants and wanting to live in the best caves. So there would have been an economic competition," said Professor Chris Stringer of the Natural History Museum in London.
It had been previously proposed that Neanderthals had been wiped out by humans in interspecies conflict or had been decimated by human disease.
Rather than disease or conflict, scientists think the Ice Age 40,000 years ago may have been the cause of extinction.