The conditions for the formation of a wake and for the onset of wake instability for the flow of power-law fluids over an unconfined circular cylinder are investigated numerically by solving the continuity and momentum equations using FLUENT (version 6.2). The effect of powerlaw index on the critical Reynolds numbers, Strouhal number and drag coefficient has been presented over a wide range of power-law index (0.3 <= n <= 1.8) thereby establishing the limits of the flow without separation and the steady symmetric flow regimes, respectively. While both the shear-thinning (n < 1) and the shear-thickening (n > 1) seem to lower the value of the critical Reynolds number denoting the onset of wake instability as compared to that for Newtonian fluids, the effect is seen to be more prominent for shear-thickening fluids than that for shear-thinning fluids. The corresponding values of the critical Stroubal number (St(c)) and drag coefficient have also been presented for the critical values of the Reynolds number. Included here are also a series of streamline plots showing the onset of asymmetry and of the time-dependent flow regime. (c) 2006 Elsevier Ltd. All rights reserved.