Daengbo's Journal: TOEFL and the Neanderthals

I was listening to someone prepare for the TOEFL exam, and a practice listening question was about Neanderthal man and inter-breeding as a possible reason for extinction. I'm pretty sure (off of the top of my head) that this theory is no longer believed, but the listening selection made me think.

What if interbreeding became popular, the offspring were sterile, and they were excluded from the homo sapien society, but not the Neanderthal one? Or the breeding may have occurred primarily between human males and Neanderthal females, for whatever reason. The breeding rate for the Neanderthal group would be greatly reduced, and the population would drop precipitously within two hundred years. No DNA evidence would be evident in modern man.