  We consider the inverse scattering problem associated with any number of
interacting modes in one-dimensional structures. The coupling between the modes
is contradirectional in addition to codirectional, and may be distributed
continuously or in discrete points. The local coupling as a function of
position is obtained from reflection data using a layer-stripping type method,
and the separate identification of the contradirectional and codirectional
coupling is obtained using matrix factorization. Ambiguities are discussed in
detail, and different {\it a priori} information that can resolve the
ambiguities is suggested. The method is exemplified by applications to
multimode optical waveguides with quasi-periodical perturbations.
