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This paper is concerned by the concept of algebra up to homotopy for astructure defined by two operations $.$ and [,]. An important example of such astructure is the Gerstenhaber algebra (commutatitve and Lie). The notion ofGerstenhaber algebra up to homotopy ($G_\infty$ algebra) is known. Here, wegive a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie)allowing the construction of $\hbox{pre}G_\infty$ algebra. Given a structure ofpre-commutative (Zinbiel) and pre-Lie algebra and working over thecorresponding dual operads, we will give an explicit construction of theassociated pre-Gerstenhaber algebra up to homotopy, this is a bicogebra(Leibniz and permutative) equipped with a codifferential which is acoderivation for the two coproducts.

Alg\`ebres pr\'e-Gerstenhaber \`a homotopie pr\`es