  This is a synopsis and extension of Phys.~Rev.~{\em D49} 5408 (1994). The
Pseudodual Chiral Model illustrates 2-dimensional field theories which possess
an infinite number of conservation laws but also allow particle production, at
variance with naive expectations---a folk theorem of integrable models. We
monitor the symmetries of the pseudodual model, both local and nonlocal, as
transmutations of the symmetries of the (very different) usual Chiral Model. We
refine the conventional algorithm to more efficiently produce the nonlocal
symmetries of the model. We further find the Canonical transformation which
connects the usual chiral model to its fully equivalent dual model, thus
contradistinguishing the pseudodual theory.
