The steady, fully developed, isothermal, incompressible laminar flow of power law fluids within a toroidal-type coiled tube has been studied for small ratio of tube radius to radius of curvature. Dean's constraint has been relaxed and the solutions of primary and secondary flows are obtained up to the second-order curvature ratio term. The expressions for primary and secondary flow of a Newtonian fluid are derived as special cases and are found to be in good agreement with published results. Comparison of the results with those of Newtonian fluids is made to bring out the effect of the power law index. The flow fields of dilatant and pseudoplastic fluids are found to differ significantly. The individual and collective roles played by the Reynolds number, curvature ratio, and power law index are discussed in detail. The results show that the flow rate of fluid in a curved tube is more influenced by curvature than by Reynolds number or power law index.