Anatomically modern humans interbred with Neanderthals and with a related archaic population known as Denisovans. Genomes of several Neanderthals and one Denisovan have been sequenced, and these reference genomes have been used to detect introgressed genetic material in present-day human genomes. Segments of introgression also can be detected without use of reference genomes, and doing so can be advantageous for finding introgressed segments that are less closely related to the sequenced archaic genomes. We apply a new reference-free method for detecting archaic introgression to 5,639 whole-genome sequences from Eurasia and Oceania. We find Denisovan ancestry in populations from East and South Asia and Papuans. Denisovan ancestry comprises two components with differing similarity to the sequenced Altai Denisovan individual. This indicates that at least two distinct instances of Denisovan admixture into modern humans occurred, involving Denisovan populations that had different levels of relatedness to the sequenced Altai Denisovan. VIDEO ABSTRACT.