  We study compactifications of string theory and M-theory to six dimensions
with background fluxes. The nonzero fluxes lead to additional mass parameters.
We derive the S- and T-duality rules for the corresponding (massive)
supergravity theories. Specifically, we investigate the massive T-duality
between Type IIA superstring theory compactified on K3 with background fluxes
and Type IIB superstring theory compactified on K3. Furthermore, we generalise
to the massive case the 6D 'string-string' S-duality between M-theory on K3 x
S^1 and the Heterotic String on T^4. Whereas in the case of massive T--duality
the mass parameters are in the fundamental representation of the U-duality
group O(4,20) we find that in the case of massive S-duality they are in the
3-index antisymmetric representation. In the latter case the mass parameters
involved extend those of Kaloper and Myers. We apply our duality rules to
massive brane solutions, like the domain wall solutions corresponding to the
mass parameters and find new massive brane solutions. Finally, we discuss the
higher-dimensional interpretation of the dualities and brane solutions.
