A recent study has been lead by Dan Dediu, who is a senior investigator in the Languages and Genetics Department of the Max Planck Institute for Psycholinguistics, based in Nijmegen in The Netherlands. The main ain of the Institute is to study the neural and genetic basis of language, as well as the cultural aspects.
     Neanderthal DNA was analysed and results showed that they possessed a gene which, in modern Man, is known to be involved in language and speech. This should be coupled with the fact that they also had a hyoid bone. This bone is located at the base of the mouth and, via muscle connections, helps the tongue to move and swallow. In addition, it allows pharyngeal and laryngeal movements which, in turn, allow a wide range of sounds to be produced.
     So did they speak like us, would we have been able to understand them? Dan Dediu has a theory "If our proposal is correct then we might not only carry some Neanderthal genes in our own genomes as traces of our past encounters, but also our languages might as well preserve some faint signature of their languages as well, but until rigorous testing is attempted, this must remain pure - even if exciting - speculation".

Edited from NBC News (11 July 2013)