  We define the notion of mirror of a Calabi-Yau manifold with a stable bundle
in the context of type II strings in terms of supersymmetric cycles on the
mirror. This allows us to relate the variation of Hodge structure for
cohomologies arising from the bundle to the counting of holomorphic maps of
Riemann surfaces with boundary on the mirror side. Moreover it opens up the
possibility of studying bundles on Calabi-Yau manifolds in terms of
supersymmetric cycles on the mirror.
