  We study in this article the concepts of algebra up to homotopy for a
structure defined by two operations $ \pt $ and $[, ]$. Having determined the
structure of $ G_\infty $ algebras and $ P_\infty $ 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
