Multihypothesis motion-compensating predictors combine several motion-compensated signals to predict the current frame signal. More than one motion-compensated signal, or hypothesis, is selected for transmission. Long-term memory motion-compensated prediction is a further concept for efficient video compression and is an example for forward-adaptive hypothesis switching. One motion-compensated signal is selected from multiple reference frames for transmission. This paper extends the theory of multihypothesis motion-compensated prediction to forward-adaptive hypothesis switching. Assume, that we combine N hypotheses. Each hypothesis that is used for the combination is selected from a set of motion-compensated signals of size M. We study the influence of the hypothesis set size M on both the accuracy of motion compensation of forward-adaptive hypothesis switching and the efficiency of multihypothesis motion-compensated prediction. In both cases, we examine the noise-free limiting case. That is, we neglect signal components that are not predictable by motion compensation. Selecting one hypothesis from a set of motion-compensated signals of size M, that is, switching among M hypotheses, will reduce the displacement error variance by factor M when we assume statistically independent displacement errors. Integrating forward-adaptive hypothesis switching into multihypothesis motion-compensated prediction, that is, allowing a combination of switched hypotheses, increases the gain of multihypothesis motion-compensated prediction over the single hypothesis case for growing hypothesis set size M.