This article uses mathematical models to investigate the consequences of noninstantaneous choice between two prey types by a predator. The models are characterized by three features: sustained cycles in predator and prey population sizes, a trade-off between the predator's consumption rates of the two prey and adaptive adjustment of the consumption rates at a rate proportional to the change in predator fitness per unit change in consumption rates. Adaptive adjustment of consumption rates frequently prevents the system from achieving an ideal free distribution of predator foraging effort and frequently results in chaotic dynamics or alternative attractors. The process of switching to consume the more common prey can reduce the minimum density of one or both prey. These phenomena occur for a variety of different models, including models in which both prey are in the same or in distinct habitats. An ideal free distribution can often be attained by adding prey refuges or immigration, provided these have a large enough effect on the dynamics of the system. The dynamics of switching can be important in determining indirect interactions between prey species and other aspects of food web dynamics.