By using quantum method the nondegenerated two-photon optical multistability equations applicable to arbitrary detunings with respect to the intermediate level have been deduced. We have put emphasis on the multistability characteristics of the pure absorption type, because this type has potentiality in pratical utility, umerical calculations have revealed some new features. It is pointed that the multistable characteristics of the two modes are different. This difference results from the difference between the upper and lower levels, A nondegenerate two-photon multistability system can be used as multi logical elements, or such a system with small intermediaie-level detuning, the operation intensity is about the same as that for the single-photon optical bistability. Therefore, it can be predicted that in the near future the nondegenerate two-photon multistability would be realized experimentally.