The Cro-Magnons may have been one important step beyond the Neanderthals in social organization.[…]That the Cro-Magnons and the Neanderthals encountered each other is probable. There seems to be no more than a five-thousand-year interval between the general occupation of home sites by the Neanderthals and their replacement by Cro-Magnon tools and fossils.
Source: wiktionary