  We discuss the analytic continuation of the Hadamard product of two
holomorphic functions under assumptions pertaining to Ecalle's Resurgence
Theory, proving that if both factors are endlessly continuable with prescribed
sets of singular points $A$ and $B$, then so is their Hadamard product with
respect to the set $\{0\}\cup A \cdot B$. In this generalization of the
classical Hadamard Theorem, all the branches of the multivalued analytic
continuation of the Hadamard product are considered.
