  We present all NSR superstring and super-D-string actions invariant under a
set of prescribed gauge transformations, and characterize completely their
global symmetries. In particular we obtain locally supersymmetric Born-Infeld
actions on general backgrounds in a formulation with extra target space
dimensions. The nontrivial global symmetries of the superstring actions
correspond to isometries of the background, whereas super-D-string actions can
have additional symmetries acting nontrivially also on the coordinates of the
extra dimensions.
