  We discuss the pseudodual chiral model to illustrate a class of
two-dimensional theories which have an infinite number of conservation laws but
allow particle production, at variance with naive expectations. We describe the
symmetries of the pseudodual model, both local and nonlocal, as transmutations
of the symmetries of the usual chiral model. We refine the conventional
algorithm to more efficiently produce the nonlocal symmetries of the model, and
we discuss the complete local current algebra for the pseudodual theory. We
also exhibit the canonical transformation which connects the usual chiral model
to its fully equivalent dual, further distinguishing the pseudodual theory.
