  We construct free field representations of the $SW$-algebras SW(3/2,2) and
SW(3/2,3/2,2) by using the corresponding Toda-Field-Theories. In constructing
the series of minimal models using covariant vertex operators, we find a
necessary restriction on the Cartan matrix of the Super-Lie-Algebra, also for
the general case. Within this framework, this restriction claims that there be
a minimum of one non-vanishing element on the diagonal of the Cartan matrix,
which is without parallel in bosonic conformal field theory. As a consequence
only two series of SSLA's yield minimal models, namely Osp(2n|2n-1) and
Osp(2n|2n+1). Subsequently some general aspects of degenerate representations
of SW-algebras, notably the fusion rules, are investigated. As an application
we discuss minimal models of SW(3/2,2), which were constructed with independent
methods, in this framework. Covariant formulation is used throughout this
paper.
