  We prove that singularities with holomorphic monodromies are preserved by
Hadamard product, and we find an explicit formula for the monodromy of the
singularities of the Hadamard product. We find similar formulas for the e\~ne
product whose monodromy is better behaved. With these formulas we give new
direct proofs of classical results and prove the invariance of interesting
rings of functions by Hadamard and e\~ne product.
