We investigate the representation theory of some recently constructed
N = 2 super W-algebras with two generators. Except for the central cha
rges in the unitary minimal series of the N = 2 super Virasoro algebra
we find no new rational models. However, from our results it is possi
ble to arrange all known N = 2 super W-algebras with two generators an
d vanishing self-coupling constant into four classes. For the algebras
existing for c greater-than-or-equal-to 3 which can be understood by
the spectral flow of the N = 2 super Virasoro algebra we find that the
representations have quantized U(1) charge.