  We discuss, in the context of the strongly coupled E_8 \times E_8 heterotic
string proposed by Horava and Witten, the appearance of anomalous U(1)_X
symmetries of a nonperturbative origin, related to the presence, after
compactification, of five-branes in the five-dimensional bulk of the theory. We
compute the gauge anomalies and the induced Fayet-Iliopoulos terms on each
boundary, which we find to be lower than the universal one induced in the
weakly coupled case.
