Leray theorem in the category of algebras over an operad

Following Milnor and Moore [8], we use graduation and filtration technics to give a direct proof of the Leray theorem in the category of P-algebras for any connected unital operad P over a characteristic zero field: any connected unital comagma in the category of P-algebras is isomorphic to a free P-algebra. (C) Academie des Sciences/Elsevier, Paris.