The effect of diblock copolymer addition on the rheological behavior and on the morphology of a PS/PMMA blend during elongation and after cessation of flow is discussed. The blends' morphology was characterized during deformation and at different stages of the relaxation process. Throughout all experiments, the copolymer concentration was selected to fall either below or above the critical concentration of interface saturation. The results show an unexpected fast relaxation at low copolymer concentration, while a much slower stress relaxation is observed at higher concentrations. Such effects were attributed to the competition between hydrodynamic convection of the copolymer molecules and the Marangoni stresses. The local entanglements of the copolymer chains were found to play a major role in such competing effects.