  We discuss the Equivalence Theorem (ET) in the BRST formalism. The existence
of a local inverse of the field transformation (at least as a formal power
expansion) suggests a formulation of the ET, which allows a nilpotent BRST
symmetry. This strategy cannot be implemented at the quantum level if the
inverse is non-local. In this case we propose an alternative formulation of the
ET, where, by using Faddeev-Popov fields, this difficulty is circumvented. We
study the quantum deformation of the associated ST identity, which turns out to
be anomaly free, and show that a selected set of Green functions, which in some
cases can be identified with the physical observables of the model, does not
depend on the choice of the transformation of the fields. In general the
transformation of the fields yields a non-renormalizable theory. When the
equivalence is established between a renormalizable and a non-renormalizable
theory, the ET provides a way to give a meaning to the last one by using the
resulting ST identity. In this case the Quantum Action Principle cannot be of
any help in the discussion of the ET. We assume and discuss the validity of a
Quasi Classical Action Principle, which turns out to be sufficient for the
present work. As an example we study the renormalizability and unitarity of
massive QED in Proca's gauge by starting from a linear Lorentz-covariant gauge.
