  We introduce a new class of nonlinear equations admitting a representation in
terms of Darboux-covariant compatibility conditions. Their special cases are,
in particular, (i) the "general" von Neumann equation $i\dot\rho=[H,f(\rho)]$,
with $[f(\rho),\rho]=0$, (ii) its generalization involving certain functions
$f(\rho)$ which are non-Abelian in the sense that $[f(\rho),\rho]\neq0$, and
(iii) the Nahm equations.
