We describe an algorithm for the concurrent comparison of three or more amino acid sequences. The basis of the approach is a progressive evaluation of selected segments from each sequence. Only a small subset of all possible segments from each sequence is compared, and a minimum of information is retained for the trace-back of the alignment. As a result, this method has the advantage of being both rapid and minimally consumptive of computer memory when constructing an alignment. This being the case, there are no practical limits on the length of sequences that may be aligned. A computer program for the alignment of three sequences is described, and this method is compared with two three-sequence extensions of the Needleman and Wunsch variety, including a recently published approach. In addition, we have made simultaneous alignments of sets of four and five sequences with this selected-segment method.