As both were species of hominin, it would have been easier for pathogens to jump populations, researchers said.
Scientists from universities of Cambridge and Oxford Brookes in the UK have reviewed the latest evidence gleaned from pathogen genomes and DNA from ancient bones, and concluded that some infectious diseases are likely to be many thousands of years older than previously believed.
There is evidence that our ancestors interbred with Neanderthals and exchanged genes associated with disease.
There is also evidence that viruses moved into humans from other hominins while still in Africa.
So, researchers argue that it makes sense to assume that humans could, in turn, pass disease to Neanderthals, and that - if we were mating with them - we probably did.
Many of the infections likely to have passed from humans to Neanderthals - such as tapeworm, tuberculosis, stomach ulcers and types of herpes - are chronic diseases that would have weakened the hunter-gathering Neanderthals, making them less fit and able to find food, which could have catalysed extinction of the species, researchers said.
"Humans migrating out of Africa would have been a significant reservoir of tropical diseases," said Charlotte Houldcroft from Cambridge University.
"For the Neanderthal population of Eurasia, adapted to that geographical infectious disease environment, exposure to new pathogens carried out of Africa may have been catastrophic," said Houldcroft.
New techniques developed in the last few years mean researchers can now look into the distant past of modern disease by unravelling its genetic code, as well as extracting DNA from fossils of some of our earliest ancestors to detect traces of disease.
Genetic data shows many infectious diseases have been "co-evolving with humans and our ancestors for tens of thousands to millions of years," researchers said.
The longstanding view of infectious disease is that it exploded with the dawning of agriculture some 8,000 years ago, as increasingly dense and sedentary human populations coexisted with livestock, creating a perfect storm for disease to spread, researchers said.
They say that many diseases traditionally thought to be 'zoonoses', transferred from herd animals into humans, such as tuberculosis, were actually transmitted into the livestock by humans in the first place.
"Hunter-gatherers lived in small foraging groups. Neanderthals lived in groups of between 15-30 members, for example. So disease would have broken out sporadically, but have been unable to spread very far," said Houldcroft.
"Once agriculture came along, these diseases had the perfect conditions to explode, but they were already around," she said.
The findings were published in the American Journal of Physical Anthropology.
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