The main purpose of this article is to give a general version of the well-known Harrtogs extension theorem for separately holomorphic functions. Using recent development in Poletsky theory of discs, the author prove the following result: Let X, Y be to complex manifolds, let Z be a complexanalytic space which possesses the Hartogs extension property, let A (resp. B) be a non locally pluripolar subset of X (resp. Y). The study show that every separately holomorphic mapping f:W:=(AxY)U(XxB) - Z extends to a holomorphic mapping f: W={(z,w)EXxY:m(z,A,X)+m(w,B,Y)I} such that f