  We consider Narain T-duality on a nontrivially fibered n-torus bundle in the
presence of a topologically nontrivial NS H flux. The action of the duality
group on the topology and H flux of the corresponding type II and heterotic
string backgrounds is determined. The topology change is specialized to the
case of supersymmetric T^2-fibered torsional string backgrounds with nontrivial
H flux. We prove that it preserves the global tadpole condition in the total
space as well as on the base of the torus fibration. We find that some of these
T-dualities exchange half of the field strength of an unbroken U(1) gauge
symmetry with the anti-selfdual part of the curvature of a physical circle
fibration. We verify that such T-dualities indeed exchange the supersymmetry
condition for the circle bundle with that of the gauge bundle.
