  Recently we investigated a new supersymmetrization procedure for the KdV
hierarchy inspired in some recent work on supersymmetric matrix models. We
extend this procedure here for the generalized KdV hierarchies. The resulting
supersymmetric hierarchies are generically nonlocal, except for the case of
Boussinesque which we treat in detail. The resulting supersymmetric hierarchy
is integrable and bihamiltonian and contains the Boussinesque hierarchy as a
subhierarchy. In a particular realization, we extend it by defining
supersymmetric odd flows. We end with some comments on a slight modification of
this supersymmetrization which yields local equations for any generalized KdV
hierarchy.
