  Let S be a generic C-infinity smooth CR manifold in C^n, n > 1, and let M be
a generic C-infinity CR submanifold of S X C^m. We prescribe conditions on M so
that it is the disjoint union of graphs of CR maps f:S-->C^m. We also consider
the special case where S is the boundary of a bounded, smoothly bounded open
set D in C^n, n > 1. In this case we obtain conditions which guarantee that
such an f above extends to be analytic on D. This provides a solution to a
particular nonlinear Riemann-Hilbert boundary value problem for analytic
functions.
