The hydrolysis of ATP catalyzed by phosphorylating vesicles prepared from bovine heart mitochondria by ultrasonic disruption was studied in H218O. Provided that an ATP-generating system was included to prevent accumulation of ADP due to hydrolysis, the addition of 20 mM arsenate or 0.5 mM 2,4-dinitrophenol to the incubation mixture either singly or together, had little or no effect on the number of oxygen atoms from H2O incorporated (on the average) into each molecule of Pi formed by hydrolysis (the O:P ratio). As the ATP concentration was reduced from 2.0 to 0.05 mM, the O:P ratio increased from about 1.4 to over 2.0 and, although dinitrophenol significantly increased the ATPase activity, it did not significantly alter the O:P ratio for a given ATP level. This implies that the uncoupler does not act directly on the terminal transphosphorylation step. Companion experiments were performed in which 18O label was placed either initially in H2O or Pi. Under conditions where extensive exchange from H218O into Pi occurred, no 18O was lost from medium Pi under identical circumstances, thus showing that the exchange was intermediate and did not involve medium Pi. Kinetic plots of v vs. v/S were nonlinear with respect to ATPase activity. The kinetic data, as well as the Pi = H218O exchange data, are consistent with enzyme models having multiple forms of catalytic sites. Several models are evaluated and attempts are made to distinguish between some of the simpler cases of these models.