Neandertal ancestry averages 1.37% in Europeans and 1.64% in East Asians. East Asians show 19.6% enrichment of Neandertal DNA over Europeans. Single admixture pulse model fails to fit fragment frequency spectrum data. Two-pulse model fits East Asian data with p=1 and European data with p=0.95. Three-pulse model has highest posterior probability of 0.55 for joint data. Additional pulses occurred after European-East Asian divergence. Dilution by Basal Eurasians not primary cause of European-East Asian difference. Complex long-term human-Neandertal interbreeding over thousands of years. Ust-Ishim genome supports admixture 52,000-58,000 years ago. Peștera cu Oase individual evidences recent Neandertal ancestor. Models reject purifying selection or population size as explanations for ancestry gap. Machine learning classifier favors multi-pulse over single-pulse or dilution models. Neandertal fragments analyzed every 100kb in 1000 Genomes data. Results robust to fragment calling errors and Denisovan misclassification. Neandertals had small effective population size promoting uniform admixture source. East-West Eurasian differences reflect varying coexistence duration with Neandertals.