The transient rheological behaviour of immiscible polymer blends is studied during start-up flows. The stresses can be divided in a contribution from the component polymers and a contribution caused by the presence of an interface. By means of relaxation measurements, the component stresses after inception of flow can be determined. In this manner, the different contributions to the stress can be compared separately with model predictions. For the contribution of the components, one normally uses mixing rules that do not take into account the morphology of the blend. As expected, a slight morphology effect can be detected. The stress contributions from the interface are calculated combining the Doi-Ohta approach with different models that describe the droplet deformation. For flows at small capillary numbers, the Maffettone-Minale model leads to accurate stress predictions. With larger capillary numbers, the normal stress profiles become more complex. The initial part is rather well described by the model of Almusallam et al. [J. Reel. 44 (2000) 1055]. It is demonstrated that the morphological changes in the blend can be deduced in quite some derail from the measured stress profiles.