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The question of complete integrability of evolution equations associated to$n\times n$ first order isospectral operators is investigated using the inversescattering method. It is shown that for $n>2$, e.g. for the three-waveinteraction, additional (nonlinear) pointwise flows are necessary for theassertion of complete integrability. Their existence is demonstrated byconstructing action-angle variables. This construction depends on the analysisof a natural 2-form and symplectic foliation for the groups GL(n) and SU(n).

On the complete integrability of completely integrable systems