The existence of an infinite set of conserved currents in completely integr
able classical models, including chiral and Toda models as well as the KP a
nd sell-dual Yang-Mills equations, is traced back to a simple construction
of an infinite chain of closed (respectively, covariantly constant) I-forms
in a (gauged) bi-differential calculus. The latter consists of a different
ial algebra on which two differential maps act. In a gauged bi-differential
calculus these maps are extended to flat covariant derivatives.