  A rigorous result about Hubbard model obtained by C.N.Yang
[Phys.Rev.Lett.63,2144(1989)] is generalized to two kinds of extended Hubbard
models. One is the Hubbard model in two-dimensional triangular lattice, and the
other is the Hubbard model for high spins fermions. We obtain the conditions
under which a modified $\eta$-pairing operator is an eigen-operator, thus these
models have a series of eigenstates possessing off-diagonal long-range order.
