Les (a,b)-alg\`ebres \`a homotopie pr\`es

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