  The five dimensional version of the Green-Schwarz mechanism can be invoked to
cancel U(1) anomalies on the boundaries of brane world models. In five
dimensions there are two dual descriptions that employ either a two-form tensor
field or a vector field. We present the supersymmetric extensions of these dual
theories using four dimensional N=1 superspace. For the supersymmetrization of
the five dimensional Chern-Simons three form this requires the introduction of
a new chiral Chern-Simons multiplet. We derive the supersymmetric vector/tensor
duality relations and show that not only is the usual one/two-form duality
modified, but that there is also an interesting duality relation between the
scalar components. Furthermore, the vector formulation always contains singular
boundary mass terms which are absent in the tensor formulation. This apparent
inconsistency is resolved by showing that in either formulation the four
dimensional anomalous U(1) mass spectrum is identical, with the lowest lying
Kaluza-Klein mode generically obtaining a finite nonzero mass.
