  We have calculated the one loop effective potential of the vector multiplets
arising from the compactification to five dimensions of heterotic M-theory on a
Calabi-Yau manifold with h^{1,1}>1. We find that extensive cancellations
between the fermionic and bosonic sectors of the theory cause the effective
potential to vanish, with the exception of a higher order curvature term of the
type which might arise from string corrections.
