  It is shown how to construct an infinite number of families of
quasi-bi-Hamiltonian (QBH) systems by means of the constrained flows of soliton
equations. Three explicit QBH structures are presented for the first three
families of the constrained flows. The Nijenhuis coordinates defined by the
Nijenhuis tensor for the corresponding families of QBH systems are proved to be
exactly the same as the separated variables introduced by means of the Lax
matrices for the constrained flows.
