Interspecific interactions may occur for just a brief period each year before the populations involved become spatially separated. For instance, the range of a migrating population may overlap with that of a population of predators for a single season. In this work, we outline a framework for examining how this kind of 'transient' predation influences the dynamics of the prey population. A time-dependent switching system is used to partition the annual cycle into distinct segments. We then consider the effect of a single predatory interaction during a particular season, with the associated predators characterised as either generalists or specialists. We show that generalist predation potentially can allow multiple stable limit cycles to exist. Predation by specialists may cause prey abundance to oscillate over long time periods. This is shown to be a consequence of over-exploitation of newborn prey individuals. The habitat-based formulation extends naturally to the study of interannual variation in environmental conditions. We illustrate how such changes may cause migrant populations to undergo sudden changes in numbers that are not readily reversible.