Nonlinear stress relaxation after imposition of step strain gamma (less than or equal to 2) was examined for blends of styrene-isoprene ISI) diblock copolymers in a homopolyisoprene (hi) matrix. The blends contained spherical micelles with S cores and I corona. For most eases, the blends had no plasticity and exhibited complete relaxation. Fast and slow relaxation processes characterizing the linear viscoelastic behavior of the micelles (part 1) were observed also for nonlinear relaxation moduli G(t,gamma). For sufficiently small gamma, G(t,gamma) agreed with the linear relaxation moduli evaluated from the G* data of part 1. However, G(t,gamma) decreased for larger gamma (mostly for gamma > 0.1). This nonlinear damping was much more significant for the slow process than for the fast process. For quantitative analysis of the damping behavior, the linear viscoelastic relaxation time tau* of the fast process was utilized to successfully separate the G(t,gamma) data into contributions from the fast and slow processes, G(f)(t,gamma) and G(s)(t,gamma), in the following way : At t > 6 tau* where the fast process had negligible contribution to G(t,gamma), G(s)(t,gamma) were taken to be identical to G(t,gamma). By extrapolating those G(s)(t,gamma) data to shorter time scales, G(s)(t,gamma) were evaluated at t < 6 tau*. G(f)(t,gamma) were evaluated as G(t,gamma) - G(s)(t,gamma). For both G(f)(t,gamma) and G(s)(t,gamma), the terminal relaxation times were insensitive to gamma and the time-strain separability held in respective terminal regions. This separability enabled us to define damping functions in those regions, h(x)(gamma) = G(x)(t,gamma)/G(x)(t) (x = f, s). For the fast process of the SI micelles, h(f)(gamma) exhibited only modest gamma dependence that was in good agreement with the dependence for homopolymer chains. This result indicated that the fast process corresponded to relaxation of individual corona I blocks, giving a strong support for the discussion of part 1. On the other hand, h(s)(gamma) of concentrated micelles exhibited very strong gamma dependence that was comparable, in both magnitudes and sensitivities to the I block concentration and molecular weight, with the dependence of the damping function h(C14)(gamma) obtained for solutions of SI in an I-selective solvent, n-tetradecane (C-14). Those solutions exhibited plasticity due to macrolattices of the micelles, and their nonlinearity was attributed to strain-induced changes in the micelle position. Thus, the similarity of h(s)(gamma) and h(C14)(gamma) suggested that the slow process of the concentrated micelles in the SI/hI blends was related to the changes in the micelle position and the subsequent micelle diffusion, again supporting the discussion of part 1.