A commutative setting for integrable theories with fermions

Graded versions of the KdV equation are shown to be equivalent to traditional hamiltonian field theories without anticommuting variables. The explicit examples here given illustrate a general procedure, which can be applied not only to super-integrable, but also to more general theories with fermions. Supersymmetry transformations are shown to correspond, in the proposed setting, to ordinary hamiltonian symmetries. (orig.)