Work has also been done on ancient anatomically modern human remains from the same time period. The mitDNA sequences of those samples was different that the neander sequences dating 3,000 years older but closely matched living human sequences. Also, there are no regional differences in neander to living human sequences. This is important since neanders have only been found in Europe and not in asia or africa. Therefore, if there was interbreeding we would expect a closer match to living europeans than to asians or africans. This is not the case, and therefore supports the case for limited or non existant interbreeding between anatomically modern humans and neanderthals.
Mammuthus's point of mitDNA being a maternal lineage and nuclear DNA being both maternal and paternal is important. However, I find it unlikely that only male neanderthals mated with human femals and human males only mated with neanderthal women when interbreeding did occur. However, the possibility does exist. Post natal development in humans and neanderthals seems to argue against interbreeding as well, which would be independent of mitDNA lineages. So far, fossil remains of neanderthal children seems to indicate a different maturation process than that seen in human populatins. If interbreeding were occuring we would expect a melding of the two maturation processes, but we find the opposite.
The only conclusion that I have been able to draw from the data is that interbreeding was not a common occurence. The possibility of occasional interbreeding still remains. Modern human lineages may only represent those lineages that survived form the period and may not reflect interbreeding lineages present at the time of neanderthal and human cohabitation of Europe. Also, the data, to this point, does support the theory that humans and neanderthals were two different species in that genetic flow between the populations was either severely limited or non-existant. Therefore, it is possible that both neanderthals and humans are both daughter species of Homo heidelbergensis.