In this paper we consider the representation theory of N = 1 Super-W-a
lgebras with two generators for conformal dimension of the additional
superprimary field between two and six. hi the superminimal case our r
esults coincide with the expectation from the ADE-classification. For
the parabolic algebras we find a finite number of highest weight repre
sentations and an effective central charge c = 2/3. Furthermore we sho
w that most of the exceptional algebras lead to new rational models wi
th c > 3/2. The remaining exceptional cases show a new 'mixed' structu
re. Besides a continuous branch of representations discrete values of
the highest weight also exist.