Score-based measures of molecular-sequence features provide versatile aids for the study of proteins and DNA. They are used by many sequence data base search programs, as well as for identifying distinctive properties of single sequences. For any such measure, it is important to know what can be expected to occur purely by chance. The statistical distribution of high-scoring segments has been described elsewhere. However, molecular sequences will frequently yield several high-scoring segments for which some combined assessment is in order. This paper describes the statistical distribution for the sum of the scores of multiple high-scoring segments and illustrates its application to the identification of possible transmembrane segments and the evaluation of sequence similarity.