  We derive the most general local boundary conditions necessary for T-duality
to be compatible with superconformal invariance of the two-dimensional N=1
supersymmetric nonlinear sigma model with boundaries. To this end, we construct
a consistent gauge invariant parent action by gauging a U(1) isometry, with and
without boundary interactions. We investigate the behaviour of the boundary
conditions under T-duality, and interpret the results in terms of D-branes.
