Summary: Testing homogeneity is a fundamental problem in finite mixture models. It has been investigated by many researchers and most of the existing works have focused on the univariate case. In this article, the authors extend the use of the EM-test for testing homogeneity to multivariate mixture models. They show that the EM-test statistic asymptotically has the same distribution as a certain transformation of a single multivariate normal vector. On the basis of this result, they suggest a resampling procedure to approximate the P-value of the EM-test. Simulation studies show that the EM-test has accurate type I errors and adequate power, and is more powerful and computationally efficient than the bootstrap likelihood ratio test. Two real data sets are analysed to illustrate the application of our theoretical results.