Rapid-equilibrium rate equations are derived for the five different mechanisms for the enzymatic catalysis of A + B + C -> products using a computer. These rate equations are used to determine the minimum number of velocities required to estimate the values of the kinetic parameters. The rate equation for the completely ordered mechanism involves four kinetic parameters, and the rate equation for the completely random mechanism involves eight kinetic parameters. Therefore, the four to eight kinetic parameters can be estimated by determining four to eight velocities and solving four to eight simultaneous equations. General recommendations are made as to the choices of triplets of substrate concentrations {[A], [B], [C]} to be used to determine the velocities. The effects of 5% errors in the measured velocities, one at a time, are calculated and are summarized in tables. Calculations of effects of experimental errors are useful in choosing the triplets of substrate concentrations to be used to obtain the most accurate values of the kinetic parameters. When the kinetic parameters for A + B + C -> products are to be determined for the first time, it is recommended that the program for the completely random mechanism be used because it can identify the mechanism and determine the kinetic parameters in one operation.