Hydrolysis of vesicles of 1,2-dimyristoyl-sn-glycero-3-phosphomethanol (DMPM) by pig pancreatic phospholipase A2 (PLA2) occurs in a highly processive "scooting" mode, and the rate is comparable to or exceeds the rates observed with detergent-dispersed mixed micelles under optimal conditions. A complete kinetic description of the steady-state time course of the hydrolysis is developed. The analysis covers the whole Michaelis-Menten space: it emphasizes the key features of interfacial catalysis by a detailed theoretical analysis, describes the experimental protocols to determine the values of the kinetic and equilibrium constants for interfacial catalysis, and provides an interpretation of the effect of calcium, substrate, products, apparent activators, and competitive inhibitors on the reaction progress curve by a single set of rate and equilibrium parameters. In this paper, the integrated reaction progress curve was rigorously interpreted in terms of a minimal model involving the Michaelis-Menten reaction sequence in the interface: E* + S in equilibrium E*S----E*P in equilibrium E* + P, and most of the individual rate and equilibrium constants for the catalytic cycle were determined. This rigorous description of interfacial catalysis was made experimentally possible by examining the action of PLA2 in the scooting mode under conditions of at most one enzyme per vesicle, where it hydrolyzed all of the substrate in the outer monolayer of vesicles without leaving the surface. Other experimentally verified constraints for this analysis include the following: all enzyme was bound to vesicles; the integrity of vesicles was maintained during the course of hydrolysis; and the substrate, enzyme, and products did not exchange between vesicles nor did they exchange across the bilayer. The mechanistic significance of the rate constants is discussed in the accompanying papers.