Mezmaiskaya Cave has yielded more than 10,000 artifacts, thousands of very well preserved faunal remains, and hominin remains, found in seven Middle Paleolithic (Mousterian) and three Upper Paleolithic levels. A complete Neanderthal infant skeleton was preserved in anatomical juxtaposition lying on a large limestone block, overlain by the earliest Mousterian layer, Layer 3. Twenty-four skull fragments from a 1-2 year-old Neanderthal infant, showing post-mortem deformation, occurred in a pit originating in the Mousterian Layer 2 and penetrating into underlying layers 2A and 2B(1). Bone from Layer 2A was dated by AMS 14C at 35.8-36.3+/-0.5 kyr BP. Direct dating of Neanderthal bone from Layer 3 gave an age of 29 kyr, but that is now considered to be due to contamination by modern carbon. Fourteen large mammal teeth from Layers 2 through 3 have been dated by standard electron spin resonance (ESR). Low U concentrations in both the enamel and dentine ensure that ESR ages do not depend significantly on the U uptake model, but do depend strongly on the sedimentary dose rates. Assuming a sedimentary water concentration equal to 20 wt%, ESR ages for the Mousterian layers range from 36.2 to 73.0+/-5.0 ka.