We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations.The main tools in our study are the maximal monotone property ofthe derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities,which generalize and extend previously known theorems.