We propose a rheological model for ideal thixotropy, defined as a reversible time-dependent shear-thinning viscous response, in both shear rate-controlled (RC Model) and stress-controlled (SC Model) forms. The model introduces a spectrum of structure parameters that collectively relaxes as a stretched exponential. It retains time-invariance symmetry with only a stretching exponent beta as an additional model parameter relative to conventional single-structure-parameter models. The kinetic equations are nonlinear in both the structure parameters and the flow parameters of strain rate or stress. We demonstrate that introducing multiple structure parameters can successfully capture the stretched-exponential and nonmonotonic evolution of stress or shear rate in general step tests; and using nonlinear kinetic equations can explain the relaxation time's dependence on both the initial and final values of shear rate or stress in step tests. We present rheological data for a fumed silica dispersion in a number of shear histories including steady state, step shear rate, step stress, shear-rate ramp, and stress ramp. A systematic way to parameterize the models is provided. Both models fit experimental data well although the SC Model provides better agreement with the measurements. The ideal thixotropic models can be combined with existing methods that incorporate viscoelasticity so as to extend their validity into the region of low shear rates. (C) 2016 The Society of Rheology.