In this talk I will consider the one-way MANOVA problem. That is, the goal is to test the null hypothesis that several groups of multivariate observations share a common center. A standard test statistic is Wilk's Lambda which corresponds to the likelihood ratio statistic under the assumption that the groups are multivariate normal with a common covariance matrix. Clearly, the classical Wilk's Lambda test is very sensitive to outliers. Therefore, robust likelihood ratio type test statistics based on high-breakdown estimators of multivariate location and scatter are proposed. In particular, test statistics based on S or MM-estimators of location and scatter will be investigated. To estimate the p-value corresponding to the test statistics, their asymptotic distribution under the null hypothesis can be used. Alternatively a fast and robust bootstrap procedure can be used to estimate the finite-sample null distribution of the test statistics. Conditions will be given under which the fast and robust bootstrap consistently estimates this null distribution. Finally, I will show some results of simulations that investigate the finite-sample properties of the resulting robust test procedures, such as their robustness and power.