In this paper we report on the nonlinear rheology of wormlike micelles in their nematic phase. Also called equilibrium or ‘‘living’’ polymers, the micelles investigated here are long, flexible, and locally cylindrical aggregates made of surfactant molecules. It is demonstrated that when subjected to a shearing flow at a constant rate, the stress response of a nematic solution of living polymers exhibits a transient regime which consists of damped oscillations, followed by a stationary regime. Peculiar attention has been paid to the transient behavior at low shear rates (γ̇<5 s−1). In this regime, it is shown that the mesoscopic domain theory developed by Larson and Doi [J. Rheol.35, 539–563 (1991)] for textured materials applies to the present micellar system. The scaling laws predicted for the transient shear stress in the tumbling regime are, for instance, well verified. When expressed in terms of strain γ=γ̇tapplied to the solution at timet, the shear stress normalized to its long time value essentially depends on the ratio γ̇/γ̇preshwhere γ̇preshdenotes the shear rate at which the solution has been presheared. This result suggests that the effect of the rheological history experienced by a nematic solution before any measurements is crucial. On the other hand it means that a constant deformation (230 strain units in the present case) is necessary for the sample to forget its shear history. As far as the rheological properties are concerned, the present study emphasizes the strong analogy between the nematic equilibrium polymers and the liquid‐crystalline polymers (LCPs). The overall rheological data are also discussed in terms of tumbling instability and flow‐alignment regime and compared to the theoretical predictions and experimental findings on LCPs. Finally, the present data suggest that the rheology of the nematic living polymers is entirely dominated by the dynamics of the textures (or defects). In contradistinction with what was originally thought, the microscopic processes such as the reversible breaking of the micellar chains seem to play a minor role here.