The dynamical processes of a Newtonian spherical drop rising freely through shear-thinning fluids expressed by the generalized Cross-Carreau (Carreau-Yasuda) model were considered experimentally and computationally. The local effects of shear-thinning on the drop motion, which are hard to evaluate from an experimental approach, are clearly revealed by the numerical results. The relation between the drop motion and the change in viscosity is clearly indicated and considered in detail for the cases in which the non-Newtonian fluids are highly and weakly pseudoplastic. In addition, the modified Reynolds and Morton numbers are discussed in order to describe the drop or bubble free motion in shear-thinning fluids using a more convenient and practical form. (C) 2003 Elsevier B.V. All rights reserved.