Covariant construction of N=1 super W-algebras

In the first part of this paper we present the general structure of Osp(1/2) invariant superconformal algebras. We show how Osp(1/2) invariance put severe constraints on the operator product expansion of two superconformal fields. Then we introduce Osp(1/2) invariant normal ordered products and apply the whole formalism to the construction of extensions of the N = 1 Super Virasoro algebra, so-called Super W-algebras. We compute explicitly the first Super W-algebra with three generators, the SW (3/2, 3/2, 2) algebra. This algebra for generic values of the central charge and one additional free parameter. (orig.)