In this paper, drop dynamics at start-up and after cessation of slow shear flows is investigated in the case of a Newtonian dispersed phase and a viscoelastic external fluid. Experimental data are taken with a rheo-optical parallel plate-shearing device, allowing for drop observation under microscopy along the vorticity direction of the shear flow. At a fixed viscosity ratio (drop to matrix viscosity is unity), experimental results of drop deformation showing the effects of varying the flow rate, though always remaining at low shear rates, and of varying the "elasticity content" of the system will be presented. Comparison of these data with predictions from two recently proposed phenomenological models of drop dynamics will also be presented and discussed. (c) 2005 Elsevier B.V. All rights reserved.