We investigate the additional symmetries of several supersymmetric KP
hierarchies: the SKP hierachy of Manin and Radul, the SKP2 hierarchy,
and the Jacobian SKP hierarchy. In all three cases we find that the al
gebra of symmetries is isomorphic to the algebra of superdifferential
operators, or equivalent SW 1 + infinity. These results seem to sugges
t that despite their realization depending on the dynamics, the additi
onal symmetries are kinematical in nature.