Three-dimensional linear stability analysis of Couette flow between two coaxial cylinders for shear-thinning fluids with and without yield stress is performed. The outer cylinder is fixed and the inner one is rotated. Three rheological models are used: Bingham, Carreau and power-law models. Wide range of rheological, geometrical and dynamical parameters is explored. New data for the critical conditions are provided for Carreau fluid. In the axisymmetric case, it is shown that when the Reynolds number is defined using the inner-wall shear-viscosity, the shear-thinning delays the appearance of Taylor vortices, for all the fluids considered. It is shown that this delay is due to reduction in the energy exchange between the base and the perturbation and not to the modification of the viscous dissipation. In the non axisymmetric case, contrary to Caton [1], we have not found any instability. (C) 2012 Elsevier B.V. All rights reserved.