  We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng
and Mas-Ramos is underpinned by the Lie-Poisson property of the second
Gel'fand-Dickey bracket. The supersymmetric Kupershmidt-Wilson theorem is also
proved along these same lines. Finally we comment on the possible repercussions
in the problem of the coproduct for W-algebras.
