  A systematic construction of super W-algebras in terms of the WZNW model
based on a super Lie algebra is presented. These are shown to be the symmetry
structure of the super Toda models, which can be obtained from the WZNW theory
by Hamiltonian reduction. A classification, according to the conformal spin
defined by an improved energy-momentum tensor, is dicussed in general terms for
all super Lie algebras whose simple roots are fermionic . A detailed discussion
employing the Dirac bracket structure and an explicit construction of
W-algebras for the cases of $OSP(1,2)$, $OSP(2,2)$ , $OSP(3,2)$ and $D(2,1 \mid
\alpha )$ are given. The $N=1$ and $N=2$ super conformal algebras are discussed
in the pertinent cases.
