This paper presents a receiver structure employing multiple receiving antennas and reduced-state Viterbi detection. The presentation is couched in terms of matrices representing a discrete-time, symbol-sampled system with frequency-selective, slow fading and additive Gaussian noise. The receiver design involves determining two matrices: one matrix defining the metric of the reduced-state Viterbi detector and one representing a pre-processor operating on the output from a maximal-ratio combiner. The presented receiver is a generalization of those used earlier in single-antenna, combined linear-Viterbi equalizers for continuous transmission systems. Performance comparisons are made with the minimum mean-square error (MMSE) linear equalizer and the MMSE decision-feedback equalizer for block transmission systems, indicating that the presented class of receivers offers superior performance