[null and void]

Making, of course, the assumption that Homo Sapiens Neanderthalensis and Homo Sapiens Sapiens really are different species.

[Verginius Rufus]

Those who believe that the Neanderthals were a different species call them Homo neanderthalensis (no sapiens in the name).

There are some studies which claim that a small amount of DNA in some modern-day people is of Neanderthal origin, but that may be disputed. The last I recall is that the common ancestor of our species and the Neanderthals was about 500,000 years ago--but opinions may vary on that.

There is a very good recent book on the Neanderthals (by that title) by Friedemann Schrenk and Stephanie Muller (with an umlaut over the U), originally in German but an English translation was published in 2009.