  We report on investigations of local (and non-local) charges in bosonic and
supersymmetric principal chiral models in 1+1 dimensions. In the bosonic PCM
there is a classically conserved local charge for each symmetric invariant
tensor of the underlying group. These all commute with the non-local Yangian
charges. The algebra of the local charges amongst themselves is rather more
subtle. We give a universal formula for infinite sets of mutually commuting
local charges with spins equal to the exponents of the underlying classical
algebra modulo its Coxeter number. Many of these results extend to the
supersymmetric PCM, but with local conserved charges associated with
antisymmetric invariants in the Lie algebra. We comment briefly on the quantum
conservation of local charges in both the bosonic and super PCMs.
