  Integrable models with higher N=2 and N=4 supersymmetries are formulated on
reductions of twisted loop superalgebras $\hat{sl}(2|2)$ and $\hat{sl}(4|4) $
endowed with principal gradation. In case of the $\hat{sl}(4|4)$ loop algebra a
sequence of progressing reductions leads both to the N=4 and N=2 supersymmetric
mKdV and sinh-Gordon equations.
  The reduction scheme is induced by twisted automorphism and allows via
dressing approach to associate to each symmetry flow of half-integer degree a
supersymmetry transformation involving only local expressions in terms of the
underlying fields.
