Using (1, 0) superfield methods, we determine the general scalar poten
tial consistent with off-shell (p, 0) supersymmetry and (1, 1) supersy
mmetry in two-dimensional non-linear sigma models with torsion. We als
o present an extended superfield formulation of the (p, 0) models and
show how the (1, 1) models can be obtained from the (1, 1)-superspace
formulation of the gauged, but massless, (1, 1) sigma model.