The circulation pattern inside fluid drops suspended in a liquid subjected to hyperbolic and to shear flow has been studied and compared with that predicted from a fluid mechanical theory which assumes that the drops remain spherical and that shear stresses are transmitted without diminution across the drop interface. Observations of liquid drops and air bubbles showed that the streamline pattern predicted for hyperbolic flow was established. The intensity of circulation in the drops was found to be decreased by impurities and added surface-active agents. Details of streamlines inside and outside drops and periods of circulation have been determined for a variety of liquid pairs in laminar shear flow. Impurities and surface-active agents exercise a pronounced inhibitory effect and often completely prevent internal circulation. In several vigorously purified systems the extent of internal circulation was less than predicted, but one liquid pair was found in which the theory was followed in all measurable details. It is shown theoretically that a viscoelastic film at the interface can reduce the shear stresses transmitted inside the drop and thus attenuate internal circulation. Calculations show that films due to surface-active materials of representative surface compressibilities are capable of completely suppressing internal circulation under the experimental conditions employed. Whereas the theory based on a nonviscous interface of zero elasticity, i.e., of constant surface tension, held for one vigorously purified system, disagreement with the theory in several others may have been due to interfacial viscosity.