The linear and nonlinear viscoelastic properties of immiscible polymer blends polypropylene/ethylenevinylacetate-ethylenemethylacryl [PP/(EVA-EMA)] have been investigated. The transient shear flow experiments reflect the structural changes of the blends during the flow. Overshoots in stress growth experiments are observed when the dispersed phase is deformable. In this case, a good description of these transient rheological data is obtained using modified versions of the Lee and Park [J. Rheol. 38, 1405 (1994)] and the Grmela and Ait-Kadi [J. Non-Newtonian Fluid Mech. 55, 191 (1994)] models. Predictions of the morphological evolution of the blend under transient shear flows were calculated from the modified models which are shown to describe the breakup and coalescence phenomena under moderately large deformation shear flow. When the dispersed phase is undeformable, these models, which are either based on the original Doi and Ohta [J. Chem. Phys. 95, 1242 (1991)] theory or derived to retrieve an extension of the Doi-Ohta theory [Lee and Park, J. Rheol. 38, 1405 (1994)], predict phase separation in contrast to the experimental evidence of stable emulsion. The Palierne emulsion model [Rheol. Acta 29, 201 (1990)] is used to characterize the linear viscoelastic properties of the blend before and after the transient shear experiments.