Modern humans and Neanderthals evolved from the same parent species (which is debated). Traditionally, Homo Erectus.

Homo Erectus lived in East Africa and spread throughout the continent and into Eurasia and Oceania. Local populations in Eurasia, cut off (or distant enough) from African population evolved gradually into Neanderthal and Denisovan, adapted to those environments.

In Africa, Erectus evolved into Sapiens, who would leave Africa following the steps of earlier Erectus, and find the descendants of them living there, the Neanderthals.

Basically, Grandma Abilis had two daughters, Erectus I and Erectus II. Erectus II left Africa for Eurasia. Erectus I had a daughter, Sapiens, who left Africa and hooked up with her cousin Neanderthal, the son of Erectus II.

This isn't an in depth answer with references - sorry for breaking the rules.

There are a lot of blurred lines when it comes to delimiting Homo species, and we can almost be considered a single chronospecies since H. erectus. However the basics of it are that the Homo genus evolved in Africa. Then, starting around 600,000 years ago, a splinter of H. heidelbergensis migrated into Europe and Asia, eventually turning into H. neanderthalensis & Denisovans respectively around 250,000-350,000 years ago*.* Meanwhile, H. heidelbergensis populations remaining in Africa were evolving into H. sapiens around the same time. It should be noted that other Homo species existed at the same time as these three, and even bred with each other, but no introgression into H. sapiens occurred.

The first successful migrations of H. sapiens out of Africa occurred around 70,000 years ago, reaching Europe and East Asia around 50,000 years ago. During this period of time, some admixing between H. sapiens, Neanderthals & Denisovans groups occurred, which persists today in H. sapiens as no more than about 10-15% of the genome for particular ethnicities.

Neanderthals & Denisovans then became extinct, while H. sapiens continued to spread into what we know today.

So, in a way, Modern Humans are both relatives and descendants of Neanderthals & Denisovans.

Here is an interesting graph that shows the evolutionary path of the Homo genus

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That has to be the BEST imagery of this explanation. So clear. Thanks

The question posed has been answered well already, so this is a pedantic post purely to satisfy myself: the term descendant is incorrect or the sentence improperly structured. You should have asked either, "Are humans descendants or relatives of Neanderthals and Denisovans?" or "Are Neanderthals and Denisovans progenitors or relatives of humans?".

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it's generally not thought that H. erectus evolved into Neandertals/Denisovans outside of Africa. Erectus was already outside of Africa long before the split separating the N/D lineage from ancestral sapiens happened within Africa.

Neandertals/Denisovans likely descended from H. heidelbergensis. A similar looking population to heidelbergensis is found in Africa, where it is sometimes called H. rhodesiensis. This population leaving Africa maybe ~700,000 years ago likely gave rise to Neandertals and Denisovans in Eurasia, while that staying behind (rhodesiensis) could have given rise to sapiens.

For comparison, Erectus is found outside of Africa (in Java) by at least 1.4 million years ago.

Interestingly, the genome of a Denisovan in Siberia showed small traces of an even older genome. This may have been from interbreeding with erectus.

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Since 1.3 million years, more than 50% of hominid finds come from europe and asia, so perhaps the African origin since 1mn years is overstated in the fog of 50 subspecies of which we know half a dozen. Neanderthal and Denisovan arent reported in africa, althought their roots are perhaps 70% african from 500k yrs.