We report on the nonlinear rheological and optical responses of a micellar viscoelastic solution of 0.3 M cetyltrimethylammonium bromide in water with a mineral salt, 1.79 M sodium nitrate, subjected to different steplike shear rates. This solution, which can be described in the regime of small deformations by the Maxwell model with a single relaxation time (tau(R)), shows a stress plateau in the experimental flow curve (sigma(gamma)) beyond a critical shear rate gamma(cl). This behavior, characteristic of a system undergoing a phase transition of the shear banding type, is corroborated by steady-state flow birefringence experiments. The transient shear stress profiles (sigma(t)) recorded after the startup of flow are very similar to those previously published on the cetylpyridinium chloride/sodium salycilate system. Just after the inception of the flow, sigma quickly increases with time and then relaxes toward its stationary value. This relaxation mechanism occurs on two different time scales and has been interpreted as follows: for duration on the order of a few TR, the purely mechanical response of the fluid is observed (overshoot and eventually damped oscillations), while for t much greater than tau(R), a long sigmoidal decay toward the plateau value occurs, which is typical of nucleation and growth of shear-induced phase processes. Time-dependent measurements of the birefringence intensity and the extinction angle confirm the existence of such an evolution. However, direct visualization of the gap shows that the growth of the induced phase is not associated with the behavior of the stretched exponential, since it occurs after the steady state in stress and optical anisotropy is achieved. The spatial distribution of the transmitted light intensity through the gap indicates that the flow is locally nonhomogeneous: the shear-induced band is made up of small sub-bands closely aligned in the flow direction.