Denisova Cave in the Siberian Altai (Russia) is a key site for understanding the complex relationships between hominin groups that inhabited Eurasia in the Middle and Late Pleistocene epoch. DNA sequenced from human remains found at this site has revealed the presence of a hitherto unknown hominin group, the Denisovans1,2, and high-coverage genomes from both Neanderthal and Denisovan fossils provide evidence for admixture between these two populations3. Determining the age of these fossils is important if we are to understand the nature of hominin interaction, and aspects of their cultural and subsistence adaptations. Here we present 50 radiocarbon determinations from the late Middle and Upper Palaeolithic layers of the site. We also report three direct dates for hominin fragments and obtain a mitochondrial DNA sequence for one of them. We apply a Bayesian age modelling approach that combines chronometric (radiocarbon, uranium series and optical ages), stratigraphic and genetic data to calculate probabilistically the age of the human fossils at the site. Our modelled estimate for the age of the oldest Denisovan fossil suggests that this group was present at the site as early as 195,000 years ago (at 95.4% probability). All Neanderthal fossils—as well as Denisova 11, the daughter of a Neanderthal and a Denisovan4—date to between 80,000 and 140,000 years ago. The youngest Denisovan dates to 52,000-76,000 years ago. Direct radiocarbon dating of Upper Palaeolithic tooth pendants and bone points yielded the earliest evidence for the production of these artefacts in northern Eurasia, between 43,000 and 49,000 calibrated years before present (taken as uc(ad) 1950). On the basis of current archaeological evidence, it may be assumed that these artefacts are associated with the Denisovan population. It is not currently possible to determine whether anatomically modern humans were involved in their production, as modern-human fossil and genetic evidence of such antiquity has not yet been identified in the Altai region.