The purpose of this paper is to develop a stochastic calculus of variations for R n -valuedstrong Markov processes with jumps x t ,which is the analogous of the Malliavin calculus of variations on diffusions. An integration by parts formula is established on a non Gaussian infinite dimensional probability space, in order to prove regularity of the probability law on R n of x t ,for fixed time t. Diffusions with jumps are also considered. The connection between the calculus of variations and the representations of martingales for jump process is exhibited.