  As generalizations of the fermion seniority model, four multi-mode
Hamiltonians are considered to investigate some of the consequences of the
pairing of parafermions of order two. 2-particle and 4-particle states are
explicitly constructed for H_A = - G A^+ A with A^+}= 1/2 Sum c_{m}^+ c_{-m}^+
and the distinct H_C = - G C^+ C with C^+}= 1/2 Sum c_{-m}^+ c_{m}^+, and for
the time-reversal invariant H_(-)= -G (A^+ - C^+)(A-C) and H_(+) = -G
(A^+dagger + C^+)(A+C), which has no analogue in the fermion case. The spectra
and degeneracies are compared with those of the usual fermion seniority model.
