As I understand it, Neanderthalers (Homo sapiens neanderthalensis) were early contemporaries of early members of our own sub species (homo sapiens sapiens) and are not ancestral to us. We all apparently came out of Africa at a variety of time periods. Homo Neanderthalensis leaving earlier than our own ancestors, though there is some doubt over the timing as to when this happened. I don't take any of the research as being anything like finalised as it is a developing area of research; further complicated by the discovery of other Archaic members of the Homo clan.