  The non-equilibrium steady states of integrable models are believed to be
described by the Generalized Gibbs Ensemble (GGE), which involves all local and
quasi-local conserved charges of the model. In this work we investigate
integrable lattice models solvable by the nested Bethe Ansatz, with group
symmetry $SU(N)$, $N\ge 3$. In these models the Bethe Ansatz involves various
types of Bethe rapidities corresponding to the "nesting" procedure, describing
the internal degrees of freedom for the excitations. We show that a complete
set of charges for the GGE can be obtained from the known fusion hierarchy of
transfer matrices. The resulting charges are quasi-local in a certain regime in
rapidity space, and they completely fix the rapidity distributions of each
string type from each nesting level.
