We study the dynamics of a slippery spherical particle suspended in an inertialess Newtonian or viscoelastic shear-thinning fluid, under shear or Poiseuille flow, by means of 3D direct numerical simulations. In particular, we investigate on the effect of particle slip on the cross-stream migration induced by fluid viscoelasticity. The governing equations are solved through the finite element method, by adopting an Arbitrary Lagrangian-Eulerian (ALE) formulation to handle the particle motion. In shear flow, the migration dynamics is qualitatively unchanged as compared to the no-slip case, i.e. the particle always moves toward the nearest wall regardless of the initial position. For increasing slip, the migration velocity first reaches a maximum, and then decreases to values lower than the no-slip one. Thus, a pronounced particle slip slows down the migration phenomenon. In Poiseuille flow, at variance with the no-slip case for a shear -thinning viscoelastic fluid, the tube wall becomes a 'hydrodynamic repulsor' for high slip values, and all the particles migrate toward the channel centerline ('attractor'). In this sense, slippery particles are more easily aligned along the channel centerline than no-slip particles. (C) 2015 Elsevier B.V. All rights reserved.