  The masses of quarks and leptons suggest a strong hierarchical structure. We
argue that their patterns can be reproduced through the introduction of a new
Abelian symmetry. The data suggest that this symmetry is anomalous. We suggest
that the cancellation of its anomalies occur through the Green-Schwarz
mechanism. An important check of this idea is that it links the Weinberg angle
to a mass ratio of the elementary fermions. The Green-Schwarz mechanism occurs
naturally in many superstring compactifications, and produces a small
parameter, which we use to determine the quark mass hierarchy. We show that
hierarchy and mixings among the chiral fermions is a consequence of the
Green-Schwarz mechanism. We present several models where this idea is realized.
