In this paper the breakup of droplets under shear in polymer blends is studied by means of linear conservative dichroism and small angle light scattering. More specifically breakup of long fibrils by interfacial instabilities is considered. Measurements are performed on dilute model systems containing nearly Newtonian components in transient flows that involve a sudden increase or decrease in shear rate. The experimental results are used to evaluate the Khakhar and Ottino theory [Khakhar and Ottino (1987)]. In this theory breakup times are calculated starting from the onset of the instability. It is demonstrated that the scaling derived from the Khakhar and Ottino theory also holds for the more readily accessible total breakup time, calculated from the onset of shear flow in a startup flow. The development of interfacial disturbances is studied in a flow history, which consists of generating fibrils by suddenly applying a shear rate followed by a sudden drop in shear rate during which the breakup process is observed. The evolution of the dominant wavelength during this process turns out to be time controlled rather than strain controlled as suggested by the theory.