We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge fields. Although, for $N\\geq 3$, the generalized cohomology of these N-complexes is non trivial, we prove a generalization of the Poincar\\é lemma. Several results which appeared in various contexts are shown to be particular cases of this generalized Poincar\\é lemma.