One component of the young-earth creation model is that what scientists call Neanderthals are actually misidentified humans. Sometimes you might hear young-earth leaders say something to the effect that if you dressed up a Neanderthal in a business suit and he walked down Wall Street, no one would notice the difference.
It is the old-earth creation position, however, that Neanderthals and early modern humans (Homo sapiens sapiens) are separate species. Furthermore, we would add that these species were separately created by God and that humans are not descended from Neanderthals, nor are either of them descendants of an ancient ape-like ancestor.
So how can we decide which of these approaches is correct? Thankfully, we live in the age of genetic research where we can easily put these two models to the test. If the young-earth model is correct, then we would expect there to be no genetic difference between Neanderthals and humans because, after all, they are really the same species. On the other hand, if the old-earth creation model is correct, then we would expect there to be no genetic connection between Neanderthals and humans.
Ok, so which way has the research been going? Overwhelmingly in an old-earth creation direction. For the full documentation, see Who was Adam? by Fuz Rana.
There is a very interesting update about the whole question of whether Neanderthals interbred with early humans. It's looking more and more like the answer to that question is "no" which further buttresses the old-earth creation model. Check out Fuz Rana's TNRTB entry for yesterday.
The Neanderthal-Human Soap Opera Continues