As recently demonstrated in several genetic association studies, historically small and isolated populations can offer increased statistical power due to extended link- age equilibrium and increased genetic drift over many generations. However, many such populations, like the Greenlandic Inuit population, have recently experienced substantial admixture with other populations, which can complicate the association studies. One important complication is that most current methods for performing association testing are based on the assumption that the effect of the tested ge- netic marker is the same regardless of ancestry. This is a reasonable assumption for a causal variant, but may not hold for the genetic markers that are tested in association studies, which are usually not causal. The effects of non-causal genetic markers depend on how strongly their presence correlate with the presence of the causal marker, and this may vary between ancestral populations because of different linkage disequilibrium patterns and allele frequencies. Motivated by this, we here introduce a new statistical method for association testing in recently admixed populations, where the effect sizes are allowed to depend on the ancestry of the allele.Our method does not rely on accurate inference of local ancestry, yet using simulations we show that in some scenarios it gives a dramatic increase in statistical power to detect associations. In addition, the method allows for testing for difference in effect size between ancestral populations, which can be used to determine if a SNP is causal. We demonstrate the usefulness of the method on data from the Greenlandic population.