  In this paper we present a superspace formulation of $N = 1, D = 6$
supergravity with one tensor-multiplet and an arbitrary number of vector- and
hypermultiplets, in which the bosonic abelian superforms of the theory, the
dilaton, the abelian gauge fields and the two-form are replaced by their
S-duals i.e. four, three and two-superforms respectively, in compatibility with
supersymmetry. As usual this replacement interchanges Bianchi identities with
equations of motion. This formulation holds in the presence of one tensor
multiplet and arbitrary numbers of hypermultiplets and abelian super-Maxwell
multiplets if all couplings are minimal. We determine the consistency
conditions for non-minimal couplings in $N = 1$, $D = 6$ supergravity, for
which we present a particularly significant solution, namely the one associated
with the Chern-Simons-Lorentz three-form which entails the Green-Schwarz
anomaly cancellation mechanism. In the case of non minimal couplings it is
found that the gauge fields and the two-form can still be dualized while the
dilaton has to remain a zero-form.
