  We study conditions on the topological D-branes of types A and B obtained by
requiring a proper matching of the spectral flow operators on the boundary.
These conditions ensure space-time supersymmetry and stability of D-branes. In
most cases, we reproduce the results of Marino-Minasian-Moore-Strominger, who
studied the same problem using the supersymmetric Born-Infeld action. In some
other cases, corresponding to coisotropic A-branes, our stability condition is
new. Our results enable us to define an analogue of the Maslov class and
grading for coisotropic A-branes. We expect that they play a role in a
conjectural generalization of the Floer homology.
