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Some years ago one of my students and I reported that the acetate kinase reaction is mediated by a phosphorylated form of the enzyme [R. S. Anthony and L. B. Spector, lBe 245, 6739 (1970)]. The reversible reaction between ATP and acetate to give acetyl phosphate and ADP had hitherto been thought to proceed by direct transfer of a phosphoryl group from A TP to acetate in a single-displacement reaction. But now it became clear that acetate kinase was one of that substantial number of enzymes whose mech- anism is that of the double displacement. For some reason, I began to wonder about the possibility that all enzymes, like acetate kinase, are double- displacement enzymes, and do their work by covalent catalysis. For one thing, I could not think of a single instance of an enzyme for which single- displacement catalysis had been proved, and inquiries on this point among knowledgeable friends elicited the same negative response. Moreover, it was long known that the two other kinds of chemical catalysis~homo- geneous and heterogeneous~occur through the intermediary formation of a covalent bond between catalyst and reactant. I began to feel confident that chemical catalysis by enzymes must happen the same way.