We consider in this work the enumeration of multiderangements of a multiset n={1^n₁,2^n₂,...,m^n_m} by the number of excedances. We prove several properties, including the invariance under permutations of {n₁,n₂,...,n_m}, the symmetry, the recurrence relation, the real-rootedness, and a combinatorial expansion, of the generating function d_n(x) of multiderangements by excedances, thus generalizing the corresponding results for the classical derangements. By a further extension, the generating function for multipermutations by numbers of excedances and fixed points is also given.