Unstable algebras over an operad

The aim of this article is to define and study a notion unstable algebra over an operad that generalises the classical Steenrod algebra. For we focus on case characteristic 2. We $\star$-unstable $\mathcal P$-algebras, where P$ $\star$ commutative binary operation in P$. then build functor takes module $M$ free P$-algebra generated by $M$. Under some hypotheses $M$, identify as P$-algebra. Finally, give examples result, show how use our main theorem obtain new construction modules studied Carlsson, Brown-Gitler, Campbell-Selick, into account their internal product.