The goal of this talk is to present a homology theory - the Gamma-homology - for the study of the categories of the differential graded algebras associated to an operad in any characteristic. We make explicit a small complex to compute this homology when the operad is binary and Koszul. This theory generalizes the Gamma-homology introduced by A. Robinson and S. Whitehouse for the category of commutative algebras. I will also show how Gamma-homology of algebras over an operad can be used for an obstruction theory in the context of positive characteristic.