Non-sub-Saharan Africans inherited Neanderthal DNA directly from post-Africa interbreeding. Sub-Saharan Africans show Neanderthal-like genomic regions of unclear origin. Up to 1% Neanderthal sequence in sub-Saharan Africans with recent non-sub-Saharan ancestry comes from Levant/North African migrants. Most Neanderthal homology in sub-Saharan Africans traces to AMH exodus from Africa 250kya, Neanderthal admixture yielding 6% AMH ancestry in Neanderthals. Multiple AMH out-of-Africa migrations occurred. Neanderthal-AMH gene flow was bi-directional. Genomic regions depleted of Neanderthal introgression in AMHs match AMH-depleted regions in Neanderthals. Depletions signal deleterious variant-background interactions. Such patterns mark incipient speciation between Neanderthals and AMHs.