A sequential sequence estimator for channels with finite or infinite intersymbol interference (ISI) is proposed. It consists of a whitened matched filter followed by a sequential algorithm. A key component of a sequential estimator is a suitable metric that accounts for the unequal search depth. This metric is derived for the ISI channel. Computer simulations for three different channels show that the sequential sequence estimator has considerably less computational complexity than a maximum-likelihood sequence estimator using the Viterbi algorithm (MLSE-VA), while still maintaining the optimum estimation performance of the MLSE-VA, a performance not achievable with any reduced-state Viterbi algorithm.>