The quantitative evaluation of rate and binding functions involves first the determination of the form, or degree, of the equation, and secondly the interpretation of coefficients from the equation in terms of basic rate and binding constants of the reaction mechanism, (a) A lower limit of the degree is provided by the log v (or Y) versus log S plot and the Hill plot. In the case of the allosteric mechanisms of Monod et al., a general linear plot has been developed which permits direct estimation of the degree. In addition, standard curves relating the extreme Hill slope to ratios of fractionally saturating concentrations have been developed which uniquely characterize the behavior of second-degree systems. They can be employed for the detection of higher than second-degree behavior. Similar use can be made of a set of normalized Scatchard binding curves, (b) Concerning the quantitative interpretation of coefficients, feasibility of a procedure based on near-exhaustive testing of random sets of rate constants has been demonstrated. Its application to a substrate-modifier mechanism of Botts and Morales enables an interpretation of sigmoidal rate curves in terms of ratios of elementary rate constants, (c) Positive or negative cooperativity of binding systems is described quantitatively by a coefficient of cooperativity, γ. In a second-degree system it can be evaluated with the help of the normalized Scatchard curves, (d) Some of these methods of analysis have been applied to the measurements of Changeux et al. on succinate binding to aspartate transcarbamylase and led to the proposal of a second-degree concerted allosteric mechanism for this system.