The shear stress response of the system CTAB/NaSal/water is studied using strain thixotropic loops in the low concentration regime and [NaSal]/[CTAB]I = 1. Stress response during up-shear curves depends on the ramping rate. However, stress response during down-shear curves collapses in one curve, no matter the rate used during the ramping down process; it does not depend on the history of the system. In the process of ramping up during the thixotropic loops, the system forms shear-induced structures. We were able to observe them through the scattered light produced by those structures, when the fluid is under shear in the gap of a transparent Couette cell. During the ramping down, the shear-induced structures survive until the shear rate vanishes. Models that describe the form of the up-shear and down-shear curves were presented, as well as, how thixotropic loops can give information about this kind of systems. In particular, for down-shear curves, we can define a decay shear rate constant that follows an Arrhenius temperature dependence. (c) 2007 Elsevier Inc. All rights reserved.