  The magnitude of the Fayet-Iliopoulos term is calculated for
compactifications of Type-I string theory and Horava-Witten M-theory in which
there exists a pseudo-anomalous U(1)_X. Contrary to various conjectures, it is
found that in leading order in the perturbative expansion around the
weakly-coupled M-theory or Type-I limits, a result identical to that of the
weakly-coupled E_8xE_8 heterotic string is obtained. The result is independent
of the values chosen for the Type-I string scale or the size of the M-theory
11th dimension, only depending upon Newton's constant and the unified gauge
coupling.
