Aqueous solutions of thread-like micelles of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) are known to be classified into three types depending on their rheological properties that change with the concentration ratio of salt to detergent: When the concentration of NaSal, C_S, is much lower than that of CTAB, C_D, the dynamic modulus, G^*, is similar to that of dilute polymer solutions without entanglements (Type I). With increasing salt concentration (C_S < C_D), G^* becomes similar to that of entangled semidilute polymer solutions (Type II). For the case of C_S ≥ C_D, G^* is described with the Maxwell model having a single relaxation time (Type III). In this study, nonlinear viscoelastic behavior of type II solutions was examined. G^* for the solution with C_D = 1.0×10⁻¹ molL⁻¹ and C_S = 3.25 ×10⁻² molL⁻¹ was very similar to that of the ordinary entangled polymer solutions. The damping function determined from the stress relaxation experiments was close to that of the entangled polymers and well described with the Doi-Edwards model. The characteristic time for nonlinear rheology, τ_eq, was determined from the stress overshoot of viscosity growth function. τ_eq was found to be about thirty times smaller than the characteristic time for nonlinear stress relaxation. These features were in accord with those of the ordinary entangled polymer solutions. However, shear rate dependence of the steady viscosity was not described with the Cox-Merz rule, suggesting that a shear induced structure might have been developed at long times during a steadily flowing state.