The catalysis of the hydration of fumarate and dehydration of i-malate by fumarase has been studied spectrophotometrically over a range of substrate concentrations of 0.1 to 10 M for i-malate and 0.1 to 3 X 10 ¯5 M for fumarate. When fumarate is the substrate linear Lineweaver-Burk plots are obtained at low substrate concentrations, but at higher concentrations the velocities are greater than expected. This effect is interpreted in terms of the alteration of the catalytic properties of the enzyme by the binding of substrate at neighboring sites which affect the enzymatic sites. Michaelis constants and maximum initial velocities for both substrates have been determined at low substrate concentrations over a pH range of 5.5 to 8.5 at phosphate buffer concentrations of 5, 15, 50, 60 and 133 mM. Although the kinetic constants vary considerably with the pH and phosphate concentration this variation is such that the Haldane relation between the kinetic constants for the two substrates and the equilibrium constant for the over-all reaction is always obeyed. The maximum initial velocities (V) increase with phosphate concentration and approach a value independent of phosphate concentration. Plots of V vs. pH are quite symmetrical bell-shaped curves as would be expected for the case where there are two ionizable groups in fumarase which are essential for its activity. The fact that the Michaelis constants (Km) for both substrates vary strongly with the pH and are nearly directly proportional to the concentration of phosphate buffer at a given pH shows that they may not be given the usual simple interpretation. The results are interpreted in terms of a mechanism which allows specifically for interaction between the enzyme and a component of the buffer.