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Most concentrated colloidal suspensions such as cement, drilling fluids, paints, muds, etc., have been considered until now thixotropic fluids with a flow curve of an ideal yield stress fluid. We start by showing from inclined plane tests, intended to determine the yield stress, that these systems in fact exhibit peculiar properties. Unlike ideal yield stress fluids, they stop flowing abruptly below a critical stress, and start flowing at a high velocity beyond a critical stress, which in addition increases with the time of preliminary rest. In order to clarify these features we carried out a complete set of rheometrical tests with a model fluid, a bentonite suspension. Our results show that under controlled stress, in some cases after significant flow, there is bifurcation of the behavior towards either stoppage or rapid shear, depending on the relative values of the imposed and critical stresses. As an immediate consequence, we find that no …