  A class of recently introduced multi-states XX models is generalized to
include a deformation parameter. This corresponds to an additional
nearest-neighbor CC interaction in the defining quadratic hamiltonian. Complete
integrability of the one-dimensional models is shown in the context of the
quantum inverse scattering method. The new R-matrix is derived. The
diagonalization of the XXC models is carried out using the algebraic Bethe
Ansatz.
