  We describe the complete coupling of $(1,0)$ six-dimensional supergravity to
tensor, vector and hypermultiplets. The generalized Green-Schwarz mechanism
implies that the resulting theory embodies factorized gauge and supersymmetry
anomalies, to be disposed of by fermion loops. Consequently, the low-energy
theory is determined by the Wess-Zumino consistency conditions, rather than by
the requirement of supersymmetry. As already shown for the case without
hypermultiplets, this procedure does not fix a quartic coupling for the
gauginos. With respect to these previous results, the inclusion of charged
hypermultiplets gives additional terms in the supersymmetry anomaly. We also
consider the case in which abelian vectors are present. As in the absence of
hypermultiplets, abelian vectors allow additional couplings. Finally, we apply
the Pasti-Sorokin-Tonin prescription to this model.
