A novel approach for modeling the mechanical behavior of thixotropic viscoplastic fluids is presented. Non-monotonic flow curves, stress overshoot during microstructure breakdown flows at constant shear rate, and viscosity bifurcation are some of the common aspects of structured fluids that are predicted by the new model. It involves two evolution equations, one for the stress and the other for the structure parameter. Simple ideas are employed to describe the microstructure. and. as a result, a model with a clear physical basis is obtained. In addition to the flow curve, which by construction is exactly predicted, it is shown that the model is able to predict correctly the behavior observed in the usual rheometric transient flows, among which abrupt changes in shear rate (microstructure buildup or breakdown experiments) and abrupt changes in shear stress (viscosity bifurcation experiments). The model is frame-indifferent and applicable to complex flows. (C) 2009 Elsevier B.V. All rights reserved.