The Neanderthals lived in Europe together with the Cro-Magnon invaders for 10,000 years until about 30,000 years ago when they became extinct. Land changed hands from Neanderthals to Cro-Magnons at a rate of only a few kilometers in a lifetime. Was this a war or did the two types of people mix? It seems unlikely that over such a long period of gradual replacement of one people by another, that no interbreeding took place.
In other places where a gradual invasion has taken place, such as in Australia, a racial mixing has occurred both on an involuntary and on a voluntary basis. Over a very long time frame, there is a tendency for everyone to take part in this mixing.
We are all Neanderthals to a greater or lesser degree. A give-away sign is the "bony ledge across the nape of the neck" (Ronald Wright "A Short History of Progress").
The large-brained Neanderthals are believed by some to have been completely eliminated by the smaller-brained modern humans.