  The chiral and scale anomalies of a very general class of non local Dirac
operators are computed using the $\zeta$-function definition of the fermionic
determinant. For the axial anomaly all new terms introduced by the non locality
are shown to be removable by counterterms and such counterterms are also
explicitly computed. It is verified that the non local Dirac operators have the
standard minimal anomaly in Bardeen's form.
