  We present a manifestly supersymmetric procedure for calculating the
contributions from matter loops to the mixed K\"{a}hler-gauge and to the mixed
K\"{a}hler- Lorentz anomalies in $N=1, D=4$ supergravity-matter systems. We
show how this procedure leads to the well-known result for the mixed
K\"{a}hler-gauge anomaly. For general supergravity-matter systems the mixed
K\"{a}hler-Lorentz anomaly is found to contain a term proportional to ${\cal
R}^2$ with a background field dependent coefficient as well as terms
proportional to $(C_{mnpq})^2$ and to the Gauss-Bonnet topological density. We
briefly comment on the relationship between the mixed K\"{a}hler-Lorentz
anomaly and the moduli dependent threshold corrections to gravitational
couplings in $Z_N$ orbifolds.
