Steady state viscosity and thixotropy of hydrophobically modified hydroxyethyl cellulose (HMHEC) and nonassociative cellulose water solutions are studied. Although all the samples are shear thinning, only the HMHEC is thixotropic, since the migration of hydrophobes to micelles is controlled by diffusion. The Cross model fits steady state curves. The Mewis model, a phenomenological model that proposes that the rate of change of viscosity when the shear rate is suddenly changed is related to the difference between the steady state and current values of viscosity raised to an exponent, fits structure construction experiments when the exponent, n, is estimated to be around 2. The Newtonian assumption used by Mewis cannot be used here, however. This seems to be related to the fact that the thickening is due to bridged micelle formation, which is a slow process, and also to topological constraints and entanglements, which are rapid processes. The kinetic parameter was redefined to k(n) in order to make it independent of initial conditions. So, k(n) depends only on how the shear affects the structure. k(n) reaches a plateau at shear rates too low to produce structure destruction and decreases at higher shear rates.