Inertialess planar contraction flow with a Navier (linear) slip boundary condition has been studied for Newtonian and inelastic non-Newtonian fluids. For Newtonian fluids there is a region of curved streamlines as the flow adjusts from an upstream no-slip region with radial streamlines to a downstream slip-flow region that also has radial streamlines. Power-law fluids exhibit qualitatively different transverse flows for n > 0.5 and n < 0.5, with radial flow for n = 0.5; it is the downstream flow that approaches no-slip for n < 0.5, while the upstream approaches slip flow. Carreau-Yasuda fluids show a transition from Newtonian behavior upstream to power-law behavior downstream. The most interesting case is a Carreau-Yasuda fluid with n < 0.5, where the azimuthal velocity changes direction, causing significant curvature in the streamlines. The streamline curvature may be relevant to the onset of entry flow instabilities at high stress levels in polymer processing. (C) 2003 Elsevier B.V. All rights reserved.