  In this paper we consider the representation theory of N=1 Super-W-algebras
with two generators for conformal dimension of the additional superprimary
field between two and six. In the superminimal case our results coincide with
the expectation from the ADE-classification. For the parabolic algebras we find
a finite number of highest weight representations and an effective central
charge $\tilde c = 3/2$. Furthermore we show that most of the exceptional
algebras lead to new rational models with $\tilde c > 3/2$. The remaining
exceptional cases show a new `mixed' structure. Besides a continuous branch of
representations discrete values of the highest weight exist, too.
