In this paper we consider the classical problem of testing whether two samples of observations are from the same distribution. Since in many situations the data are multivariate or even of functional type, classical methodology is not applicable. In our approach we conceive a difference in distribution as the occurrence of a change-point problem, where the change-point is known in advance. This point of view enables us to construct new tests which are distribution-free under the null hypothesis for general sample spaces. The power function of the tests is studied under local and global alternatives. Finally some optimality results are provided.