Homo sapiens neandertalensis coexisted with Homo sapiens (archaic) and early H. sapiens sapiens in Europe and the Mideast for 80,000 years.

Although early modern humans expanded throughout Eurasia some time between 30,000 and 40,000 years ago, not enough evidence exists to prove where they originated. Perhaps Neanderthals in some areas were replaced by modern humans, while those in other regions evolved into modern humans on their own. And if Neanderthals in certain regions were replaced, it may be that some of the H. sapiens sapiens groups replacing them had evolved not in Africa, but somewhere in Eurasia, from a Neanderthal stock.

These different possibilities concerning the transition from Neanderthals to modern humans in Eurasia tie into a debate on the origin of humans in general. One or the other of two competing hypotheses try to solve the dilemma: the Out-of Africa theory and the the multiregional one.

Genetic studies of DNA from living people appear to support the first theory. These ones indicate a relatively recent common ancestry for all the far-flung peoples inhabiting the planet today. They also consistently show present-day Africans to be the most genetically divergent, and therefore the older, branch of humanity. These findings point toward a recent African origin for modern humans. Such investigations have been enhanced by analyses of ancient DNA from actual Neanderthal remains, proving that Neanderthal DNA differs significantly from our own.

A multiregional theory basis comes from a study involving mitochondrial DNA from bones cells of an early modern human who lived 62,000 years ago in Australia. This individual's DNA, like that of the Neanderthals', also differs from our own. His DNA sequence is more primitive than the DNA sequence which, according to the calculations of Out-of-Africa theorists, must have existed in the early modern Africans who were supposedly our ancestors. These findings both decrease the genetic divide between Neanderthals and early modern humans, and increase the likelihood that early modern humans outside Africa had non-African roots. All of this makes it more probable that Neanderthals and other archaic non-Africans were among the ancestors of modern humans.

Regardless of which of the two hypotheses is right, the explanation of an enigmatic scenario of Neanderthals replacement by early modern humans would yet remain. This is complicated by the evidence that Neanderthals themselves were gradually evolving a modern physique. They were stronger than modern man. Their tools and skillz paralleled the coexisting Homo sapiens sapiens, but it is not known who copied. Although lacking a forehead, they had brains that averaged about 8% larger than modern man. They were the first to bury their dead, complete with flowers and artifacts, and had symbolic language. However, they disappeared 30,000 years ago without merging into the H. sapiens sapiens gene pool.

Moreover speculations may be made in such a respect.
The culmination of man's evolution was Homo sapiens (archaic). He came straight and tall, hardened and practical, with almost a full size brain, the result of four million years of evolution. Humankind was now a veteran of millions of deaths and countless hardships, with a population so small that mutations spread rapidly. His gene pool had little variability. Death and misery had kept him pared. Only the strongest, the most cunning, and the most stubborn survived.

Then came modern man, an anticlimax, about 120,000 years ago. From this point on his inventive mind would devise method after method to ease his lot. He would remove his enemies without compassion. He would learn to enslave other animals and even other men. He would greedily take from the world around him and from those who were weaker. He would make his life easier, and evolution would degrade him to match.

Did Neanderthals get in the way of the Homo sapiens sapiens and were simply exterminated? Maybe.
In the end, there are loads of examples which illustrate homospecies wars among us, some of them resulting in one-opponent annihilation.

Based upon the Talk.Origins: Five Major Misconceptions about Evolution FAQ.