Multi-hypothesis motion-compensated prediction extends traditional motion-compensated prediction used in video coding schemes. Known algorithms for block-based multi-hypothesis motion-compensated prediction are, for example, overlapped block motion compensation (OBMC) and bidirectionally predicted frames (B-frames). This paper presents a generalization of these algorithms in a rate-distortion framework. All blocks which are available for prediction are called hypotheses. Further, we explicitly distinguish between the search space and the superposition of hypotheses. Hypotheses are selected from a search space and their spatio-temporal positions are transmitted by means of spatio-temporal displacement codewords. Constant predictor coefficients are used to combine linearly hypotheses of a multi-hypothesis. The presented design algorithm provides an estimation criterion for optimal multi-hypotheses, a rule for optimal displacement codes, and a condition for optimal predictor coefficients. Statistically dependent hypotheses of a multi-hypothesis are determined by an iterative algorithm. Experimental results show that increasing the number of hypotheses from 1 to 8 provides prediction gains up to 3 dB in prediction error.