We develop and test two methods for distinguishing between recent admixture and ancestral population structure as explanations for greater similarity of one of two populations to an outgroup population. This problem arose when Neanderthals were found to be slightly more similar to nonAfrican than to African populations. The excess similarity is consistent with both recent admixture from Neanderthals into the ancestors of nonAfricans and subdivision in the ancestral population. Although later studies showed that there had been recent admixture, distinguishing between these two classes of models will be important in other situations, particularly when high-coverage genomes cannot be obtained for all populations. One of our two methods is based on the properties of the doubly conditioned frequency spectrum combined with the unconditional frequency spectrum. This method does not require a linkage map and can be used when there is relatively low coverage. The second method uses the extent of linkage disequilibrium among closely linked markers.