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 puts 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 exists for generic values of the central charge and one additional free parameter.