Summary: Simulation capability on ratchetting of modified 9Cr-1Mo steel at 550 \(^\circ\)C was discussed using several constitutive models in the present paper. It was revealed that the authors’ previous model, which uses an Armstrong-Frederick kinematic hardening rule, has a strong tendency to overestimate both uniaxial and multiaxial ratchetting of the material. On the contrary, the Ohno-Wang (OW) I model tended to underestimate the uniaxial and multiaxial ratchetting. The OW II and III models predicted the uniaxial and multiaxial ratchetting with better accuracy. Regarding the uniaxial ratchetting under the zero mean stress condition described in part 1 of this study [Int. J. Plast. 21, No. 1, 43–65 (2005; Zbl 1112.74345)], none of the constitutive models was able to simulate it even qualitatively. On the basis of the OW I model, a constitutive model incorporating a tension-compression asymmetry was proposed to predict the ratchetting behavior under the zero mean stress condition. The simulation capability of the proposed model was discussed in comparison with that of the other constitutive models.