Neanderthal language similar to modern humans?

Our closest cousins - the Neanderthals - may have shared speech and language with modern humans, a new research suggests.
Fast-accumulating data seem to indicate that Neanderthals were much more similar to us than imagined even a decade ago.
The researchers Dan Dediu and Stephen C Levinson from the Max-Planck-Gesellschaft, argue that modern language and speech can be traced back to the last common ancestor we shared with the Neanderthals roughly half a million years ago.
Initially thought to be subhuman brutes incapable of anything but the most primitive of grunts, they were a successful form of humanity inhabiting vast swathes of western Eurasia for several hundreds of thousands of years, during harsh ages and milder interglacial periods, researchers said.

It is known that they were our closest cousins, sharing a common ancestor with us around half a million years ago (probably Homo heidelbergensis), but it was unclear what their cognitive capacities were like, or why modern humans succeeded in replacing them after thousands of years of cohabitation.
Due to new palaeoanthropological and archaeological discoveries and the reassessment of older data, but especially to the availability of ancient DNA, researchers have started to realise that their fate was much more intertwined with ours and that their cognitive capacities and culture were comparable to modern humans.

Dediu and Levinson argue that essentially modern language and speech are an ancient feature of our lineage dating back at least to the most recent ancestor we shared with the Neanderthals and the Denisovans - another form of humanity known mostly from their genome.

Their interpretation of the evidence goes against the scenario usually assumed by most language scientists, that of a sudden and recent emergence of modernity, presumably due to a single - or very few - genetic mutations.
This pushes back the origins of modern language by a factor of 10 from the often-cited 50 or so thousand years, to around a million years ago, researchers said.
Researchers said given that we know from the archaeological record and recent genetic data that the modern humans spreading out of Africa interacted both genetically and culturally with the Neanderthals and Denisovans, then just as our bodies carry around some of their genes, maybe our languages preserve traces of their languages too.

The paper appeared in the journal Frontiers in Language Sciences.