AbstractWe study irreducible and reducible representations of the generalized Lie algebra of Wess and Zumino. The algebra is integrated to a group with the help of Grassmann algebras and the representations of the algebra are made into representations of the group. We construct invariant sesquilinear forms that are positive definite for the Wess‐Zumino algebra over the complex field. We define irreducible superfields for any spin J as specific realizations of such representations. All superfields appearing in the literature are either equivalent to one of these or built up out of these superfields.