The phenomenon of droplet breakup in nonuniform shear flow (e.g., in a cylindrical tube) is of practical importance in many polymer processing operations. A theoretical and experimental study was carried out on the stability of a long threadlike viscoalastic droplet suspended in a viscoelastic medium flowing through a cylindrical tube. The stability analysis was carried out using linearized dynamic equations with the Jeffreys model. A perturbation method was used for the case of small wave numbers, and the case of small Reynolds numbers was also considered. A theoretical criterion for droplet breakup was obtained in terms of the rheological properties of the fluids concerned, and the flow conditions. The results reveal that a long threadlike droplet cannot be stable under all disturbances, and that both the elastic and viscous properties affect the stability of extending droplets. Furthermore, it was found that the interfacial tension tends to destabilize the extending threadline. For the experimental study, the same apparatus and fluid systems as those described in part I of this series [H. B. Chin and C. D. Han, J. Rheol., 23(5), 557–590 (1979)] were used. The breakup patterns of droplets were recorded on both movie and still films. It was observed that the droplets were elongated greatly at the entrance region of the tube and then, under certain flow conditions, broke up into smaller droplets in the cylindrical tube section. The breakup conditions were correlated to the rheological properties of the droplet phase and the suspending medium.