  It is shown that supersymmetric integrable models in two dimensions, both
relativistic (i.e. super-Toda type theories) and non-relativistic (reductions
of super-KP hierarchies) can be associated to general Poisson-brackets
structures given by superaffinizations of any bosonic Lie or any super-Lie
algebra. This result allows enlarging the set of supersymmetric integrable
models, which are no longer restricted to the subclass of superaffinizations of
purely fermionic super-Lie algebras (that is admitting fermionic simple roots
only).
