The shape evolution of a liquid drop immersed in an immiscible liquid is studied under transient flow conditions. The drop is Newtonian and buoyancy free; the external liquid is Newtonian and subjected to shear flow reversal. Three model systems, polydimethylsiloxane/polyisobutylene, polybutene/silicone oil, and silicone oil/polybutene, all Newtonian under the experimental conditions investigated, have been selected to have a range of viscosity ratios. The three drop axes and the drop orientation within the shear plane are independently measured. The results are compared with the predictions of a phenomenological model. The agreement between experimental results and theory is good. Peculiar behavior of the orientation angle has been observed and correctly predicted. The results are also used to explain some rheological features typical of immiscible polymer blends.