The motion of fluid droplets in constricted capillary tubes is investigated for flows subject to the combined action of a mean pressure gradient and an oscillatory body force. Numerical computations are employed to determine the effect of the oscillatory forcing on the mean flow rate and the mean droplet velocity. In the absence of oscillatory forcing, a critical pressure gradient for droplet propagation exists, below which droplets become plugged in the narrow constrictions of the tube. For mean pressure gradients below this threshold, oscillatory forcing is shown to be an effective means for unplugging the constrictions and remobilizing the droplets. For this remobilization process to occur, the oscillatory forcing level must exceed a specified value, and the oscillatory frequency must remain below a critical frequency. Quasi-steady models are shown to give effective predictions of the unsteady dynamics over a wide range of conditions.