Chains of two hydrogen bonds (charge-relay systems) exist in the active sites of serine proteases and may be catalytic entities. It is shown theoretically that the coupling of the motions of the two protons in such arrays (and thus the efficiency with which they can relay charge) is a critical function of the distances across the hydrogen bonds; long distances favour uncoupled motion, short distances coupled motion. Rate measurements in mixtures of light and heavy water show that the serine proteases chymotrypsin, trypsin and elastase function as one-proton catalysts, one proton of the chain presumably bridging as in ordinary general catalysis. On the other hand, three enzymes of the amidohydrolase class, a glutaminase and two asparaginases, show two-proton catalysis. This may arise from a charge-relay chain, although evidence for such a structure has not yet been advanced for these enzymes, or from some other catalytic entity involving two coupled proton bridges.