The morphology development in dilute and semi-concentrated blends (2 and 15 wt% disperse phase) of viscoelastic polymers is studied during flow in dies. In the entrance region the droplets deform into fibrils. In the die itself some of the fibrils can break up depending on their shear history and hence on their radial position. The morphology at the exit of the die is investigated by quenching the extrudate and visualizing the structure via scanning electron microscopy (SEM). For fibrils moving along the die axis, the theory of Tomotika for break-up of a fibril in a quiescent matrix describes the observations satisfactorily. Fibrils flowing off center undergo a shearing flow in the die, which could have an effect on the growth of the Rayleigh disturbances that cause break-up. It is observed that during flow break-up still occurs via Rayleigh instabilities. As a first approximation the theory of Tomotika also predicts the break-up of fibrils flowing off center, if the viscosity at the relevant shear rate is used.