  A compact 4-dimensional manifold is a non-singular graph-manifold if it can
be obtained by the glueing T^2-bundles over compact surfaces (with boundary) of
negative Euler characteristics. If none of glueing diffeomorphisms respect the
bundle structures, the graph-structure is called reduced. We prove that any
homotopy equivalence of closed oriented 4-manifolds with reduced nonsingular
graph-structures is homotopic to a diffeomorphism preserving the structures.
