We introduce a general definition of a n-crossed module of P-algebras over an algebraic operad P, which coincides with historical definitions in the cases of the operads As of Lie and n = 1. We establish a natural isomorphism between the abelian group of equivalence classes of n-crossed modules over a pair (A, M ) for an operad P and the (n + 1) th operadic cohomology group of A with coefficients in M .