Most elimination and addition reactions in biochemistry proceed by α,β-elimination/addition mechanisms. In the case of elimination, the leaving group is β to an activating functional group in the substrate. The activating group may be the carbonyl group of a ketone or aldehyde, the iminium group derived from an aldehyde or ketone, or the acyl-carbonyl of a carboxylic acid or ester, and the proton is α to the activating group. Addition reactions in this class are the same reactions in reverse, and they follow the course of the Michael addition in organic chemistry. The generic process is illustrated in scheme 9-1. Substituents among the activating and leaving groups are diverse and are presumed to account for the significant variations among enzymes in the class. A few enzymes in this class catalyze elimination/addition without the assistance of a coenzyme or cofactor. They presumably incorporate sufficiently acidic (A—H) or basic (:B) amino acid side chains to catalyze the proton transfer processes, or they may stabilize carbanionic intermediates by low-barrier hydrogen bonding. Others employ divalent metal ions, pyridoxal-5'-phosphate (PLP), [4Fe–4S] centers, or NAD+ to facilitate the reactions. Cofactors and coenzymes increase the acidity of Cα—H or improve the propensity of the leaving group Y to depart. In most cases, the major barrier consists of increasing the acidity of the Cα—H group, which decreases the pKa. In a few cases, as when the leaving group is a carboxylic acid or a phosphate, no catalysis is required for it to depart. Limited space prevents discussion of the many enzymes that catalyze cofactor-independent α, β-eliminations. We address the actions of fumarase and crotonase because of the historic emphasis on the biochemical significance of these enzymes. Many other dehydratases and ammonia lyases also belong in this group. In the tricarboxylic acid cycle, fumarate arises from the action of succinate dehydrogenase, and fumarase (EC 4.2.1.2) catalyzes the addition of water to form S-malate. The reaction can be monitored in either direction, and in various studies, the kinetic parameters may be quoted as such (e.g., fumarate formation, or malate formation). The body of knowledge about the action of fumarase is surprisingly incomplete, given the importance of the enzyme in metabolism.