  A foundational investigation of the basic structural properties of
two-dimensional anomalous gauge theories is performed. The Hilbert space is
constructed as the representation of the intrinsic local field algebra
generated by the fundamental set of field operators whose Wightman functions
define the model. We examine the effect of the use of a redundant field algebra
in deriving basic properties of the models and show that different results may
arise, as regards the physical properties of the generalized chiral model, in
restricting or not the Hilbert space as representation of the intrinsic local
field algebra. The question referring to considering the vector Schwinger model
as a limit of the generalized anomalous model is also discussed. We show that
this limit can only be consistently defined for a field subalgebra of the
generalized model.
