The present paper deals with the Taylor-Couette flow of shear-thinning fluids. It focuses on the first principles understanding the influence of the viscosity stratification and the nonlinear variation of the effective viscosity µ with the shear rateγ on the flow structure in the Taylor vortex flow regime. A wide gap configuration (η = 0.4) is mainly considered. A weakly nonlinear analysis, using the amplitude expansion method at high order is adopted as a first approach to study nonlinear effects. For the numerical computation, the shear-thinning behavior is described by the Carreau model. The rheological parameters are varied in a wide range. The results indicate that the flow field undergoes a significant change as shear-thinning effects increase. First, vortices are squeezed against the inner wall and the center of the patterns are shifted axially towards the radial outflow boundaries (z = 0, z/λ z = 1). This axial shift leads to increasing concentration of vorticity at these positions. The outflow becomes more stronger than the inflow and the inflow zone, where the vorticity is low, increases accordingly. Nevertheless, the strength of the vortices relative to the velocity of the inner cylinder is weaker. Second, the pseudo-Nusselt number, ratio of the torque to that obtained in the laminar flow, decreases. Third, higher harmonics become more relevant and grow faster with Reynolds number. Finally, the modification of the viscosity field is described.