  For Hitchin's generalised geometries we introduce and analyse the concept of
a structured submanifold which encapsulates the classical notion of a
calibrated submanifold. Under a suitable integrability condition on the ambient
geometry, these generalised calibrated cycles minimise a functional occurring
as D-brane energy in type II string theories, involving both so-called NS-NS-
and R-R-fields. Further, we investigate the behaviour of calibrated cycles
under T-duality and construct non-trivial examples.
