Just as a clarification, the fact that it seems that Neanderthals and modern humans may have produced viable offspring does not mean that they were the same species.

As an example: lions and tigers can produce viable offspring despite being separate species, with more divergence than modern humans and neanderthals.

It is still being debated by smarter people than me whether neanderthals were a separate species.

By "viable" do you mean offspring that are reproductively fertile?  Because the various hybrids of lions and tigers are almost invariably sterile.  Unlike dogs and wolves, which can interbreed quite successfully and have offspring that go on to do the same.  
Alison

I'm already way over my head on this, biology is not my strong suit. I am in danger of once again flaunting my ignorance, but that never stopped me before.

Female ligers are occasionally fertile. Female zeedonks are occasionally fertile. The percentage of neanderthal DNA in modern humans is low - in the range of 1% to 4%. Were their offspring viable and fertile because they were the same species, but they rarely interbred with other humans for social and cultural reasons? Or did they attempt interbreeding more regularly but their offspring had reduced fertility?

From what I have read there seems to be 2 schools of thought as to whether neanderthals and the ancestors of modern humans were separate species or not. Neither side is likely to give up their position in a hurry.

Check out this link to a recent article on the findings:

http://www.cosmosmagazine.com/news/3440/...page=0%2C0

The article includes this quote:

But some of the comments attached to the article seem very well informed and offer an alternative viewpoint.