  We present an N = 2 world-sheet superspace description of D-branes on
bihermitian or generalized Kaehler manifolds. To accomplish this, D-branes are
considered as boundary conditions for a nonlinear sigma-model in what we call N
= 2 boundary superspace. In this note the general formalism for such an
approach is presented and the resulting classification sketched. This includes
some remarks regarding target spaces whose parameterization includes
semi-chiral superfields which have not appeared in the literature yet. In an
accompanying note we turn to some examples and applications of the general
setup presented here.
