  Local commuting charges in sigma-models with classical Lie groups as target
manifolds are shown to be related to the conserved quantities appearing in the
Drinfeld-Sokolov (generalized mKdV) hierarchies. Conversely, the
Drinfeld-Sokolov construction can be used to deduce the existence of commuting
charges in these and in wider classes of sigma-models, including those whose
target manifolds are exceptional groups or symmetric spaces. This establishes a
direct link between commuting quantities in integrable sigma-models and in
affine Toda field theories.
