  We point out a generic problem in string-inspired supergravity models with an
anomalous $U(1)_X$. A large number of matter multiplets charged under $U(1)_X$
remain massless above the supersymmetry-breaking scale because of degeneracy of
vacua solving the D-flatness conditions. A toy model is analyzed as an
illustration of the mechanism; we find the surprising result that many scalars
remain massless after supersymmetry-breaking in a hidden sector.
