The rheological and morphological changes that are induced in emulsions or simple polymer blends by simple flow histories are relatively well understood. Here these results are extended to more complex Bow histories, which not only approach more closely real processing conditions but also provide more critical tests in model assessment. For this purpose, a semiconcentrated, incompatible, model blend is subjected to a stepwise increase in shear rate followed by a flow reversal. The blend morphology consists of droplets immersed in a matrix. Two different types of behavior are identified, depending on the instant at which the flow is reversed. When this occurs after the droplets are broken up, the stress transients resemble those of the corresponding step-up experiment. When flow is reversed prior to the droplet break-up, the stress transients are much longer than those in simple step-up experiments, the normal stress curves also become more complex. A model is presented for flow reversal prior to droplet break-up. A satisfactory agreement, albeit only qualitative, is obtained assuming that the drops deform affinely during the entire transient. As expected, tumbling of the droplets does not seem to provide an adequate description of the observed transients. The experimental results show that a residual interfacial stress is always present, thus indicating a residual mean deformation of the droplets in the flow direction during the whole transient. Polydispersity of the droplet population is proposed as a possible explanation for this phenomenon. Light scattering and conservative dichroism measurements, performed on a similar blend undergoing the same type of Bow history, confirm indeed that a residual mean stretching of the drops persists throughout the flow reversal.