According to the signal hypothesis, a signal sequence, once having initiated export of a growing protein chain across the rough endoplasmic reticulum, is cleaved from the mature protein at a specific site. It has long been known that some part of the cleavage specificity resides in the last residue of the signal sequence, which invariably is one with a small, uncharged side-chain, but no further specific patterns of amino acids near the point of cleavage have been discovered so far. In this paper, some such patterns, based on a sample of 78 eukaryotic signal sequences, are presented and discussed, and a first attempt at formulating rules for the prediction of cleavage sites is made.