We consider the displacement, in a rectangular channel, of a Newtonian oil pushed by different types of liquids (Newtonian, shear-thinning, viscoelastic) of slightly higher apparent viscosity. In the absence of viscoelastic effects the interface between the two fluids becomes sharper at larger velocities, so that the thickness of the lateral film left behind increases with the flow rate. On the contrary, with a viscoelastic fluid, the shape of the interface is almost independent of the velocity so that the thickness of the lateral film is approximately constant. Moreover this thickness decreases when the ratio of normal to tangential stresses increases, suggesting that this effect can be attributed to normal stress differences. A heuristic theoretical approach tends to confirm this statement. (C) 2013 Elsevier Inc. All rights reserved.