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We study in this article the concepts of algebra up to homotopy for a structure defined by two operations . and [ , ]. Having determined the structure of G∞ algebras and P∞ algebras, we generalize this construction and we define a structure of (a, b)-algebra up to homotopy. Given a structure of commutative and differential graded Lie algebra for two shifts degree given by a and b, we will give an explicit construction of the associate algebra up to homotopy. Résumé. Onétudie dans cet articledoi:10.5802/ambp.279 fatcat:tkwtoqjlbzcupcv266b4rkyidy