This thesis is intended for the variational study of some contact problems with or without friction, adhesion, damage and wear between two deformable bodies. We analyze dynamic processes for thermo-electro-visco-elastic, electro-visco-plastic materials.The results obtained concern the existence and uniqueness of a solutionlow for the problems studied. The thesis is structured in four chapters. The first chapter is devoted to recalling the various mechanical models of contact studied. The second chapter is as well as to recall the few mathematical tools needed in the thesis. The third chapter is dedicated to the analysis of thermo-electro-viscoelastic problems with adhesion and damage. The fourth chapter is dedicated to the analysis of electro-visco-plastic problems with friction and wear.