  We use Pauli-Villars regularization to evaluate the conformal and chiral
anomalies in the effective field theories from Z3 and Z7 compactifications of
the heterotic string without Wilson lines. We show that parameters for
Pauli-Villars chiral multiplets can be chosen in such a way that the anomaly is
universal in the sense that its coefficient depends only on a single
holomorphic function of the three diagonal moduli. It is therefore possible to
cancel the anomaly by a generalization of the four-dimensional Green-Schwarz
mechanism. In particular we are able to reproduce the results of a string
calculation of the four-dimensional chiral anomaly for these two models.
