The nonlinear relaxation modulus was examined for styrene-isoprene (SI) diblock copolymer micelles having rigid (glassy) S cores and flexible I corona blocks. These micelles, being dispersed randomly in entangling and/or nonentangling matrices of homopolyisoprene (M), exhibited fast and slow relaxation processes. The fast process reflected the orientational relaxation of the corona I blocks, and the slow process detected the relaxation of the Brownian stress sigma(B). This sigma(B) reflected the anisotropy of micelle distribution and relaxed through the micelle diffusion. The fast and slow processes exhibited the nonlinear damping of the modulus under large step strains (gamma), and the time-strain separability was observed for both processes in either the entangling or nonentangling matrices. For the fast process, the damping function hf(gamma) hardly changed with the SI micelle concentration C-SI and matrix molecular weight M-matrix and was close, in magnitude, to h(gamma) of homopolymers. The nonlinearity of the corona relaxation characterized with this h(f)(gamma) was attributed to retraction of the strain-elongated corona blocks occurring prior to their rotational motion (orientational relaxation). The damping function h(s)(gamma) of the slow process, being smaller than h(f)(gamma), decreased with increasing C-SI. This nonlinearity of the slow process, similar to that of Brownian suspensions, reflected the gamma-insensitivity of the micelle distribution anisotropy for large, and the strong C-SI dependence of h(s)(gamma) was attributed to relative rotation of concentrated micelles colliding with each other under large strains. (This rotation is similar to random mixing, thereby reducing the anisotropy and enhancing the damping.) Interestingly, the damping of the slow process was weaker in the entangling matrices than in the nonentangling matrices. This effect of the corona-matrix entanglement, observed for both the concentrated and dilute micelles with and without corona-corona entanglement, was attributed to the elasticity of the entangling matrices that disturbed the relative rotation of the mutually colliding micelles. A similar elastic effect of the corona-corona entanglement on the damping behavior was also noted.