  We discuss an ambiguity in the one-loop effective action of massive fields
which takes place in massive fermionic theories. The universality of
logarithmic UV divergences in different space-time dimensions leads to the
non-universality of the finite part of effective action, which can be called
the non-local multiplicative anomaly. The general criteria of existence of this
phenomena are formulated and applied to fermionic operators with different
external fields.
