AbstractThis article investigates the effect of shear‐thinning viscosity on chaotic mixing when the kinematics first begin to deviate from Newtonian flow. Computations are done for a 2‐D, time‐periodic flow between eccentric cylinders. The effectiveness of mixing is analyzed by examining the asymptotic coverage of a passive tracer, character and location of periodic points, and the rate of stretching of fluid elements. Small variations in the velocity field associated with non‐Newtonian kinematics produce large effects in the chaotic advection of a passive tracer. The stretching rate remains exponential, but with a long time constant as the shear‐thinning effect increases, often resulting in the birth of new periodic islands and a decrease in the asymptotic coverage of the tracer. Exceptions to these observations are possible: both the stretching rate and the asymptotic coverage might increase as shear thinning increases. Results also indicate that suitable manipulation of operating conditions can produce shear‐thinning flows which mix as well as Newtonian flows. Since significant effects are observed with less than a 4% difference in the velocity fields, the assumption of Newtonian kinematics can lead to large errors in the design and operation of process mixing equipment for non‐Newtonian fluids.