Experiments are reported on the uni-site catalysis and the transition from uni-site to multi-site catalysis with bovine heart mitochondrial F1-ATPase. The very slow uni-site ATP hydrolysis is shown to occur without tightly bound nucleotides present and with or without Pi in the buffer. Measurements of the transition to higher rates and the amount of bound ATP committed to hydrolysis as the ATP concentration is increased at different fixed enzyme concentrations give evidence that the filling of a second site can initiate near maximal turnover rates. They provide rate constant information, and show that an apparent Km for a second site of about 2 microM and Vmax of 10 s-1, as suggested by others, is not operative. Careful initial velocity measurements also eliminate other suggested Km values and are consistent with bi-site activation to near maximal hydrolysis rates, with a Km of about 130 microM and Vmax of about 700 s-1. However, the results do not eliminate the possibility of additional 'hidden' Km values with similar Vmax:Km ratios. Recent data on competition between TNP-ATP and ATP revealed a third catalytic site for ATP in the millimolar concentration range. This result, and those reported in the present paper, allow the conclusion that the mitochondrial F1-ATPase can attain near maximal activity in bi-site catalysis. Our data also add to the evidence that a recent claim, that the mitochondrial F1-ATPase does not show catalytic site cooperativity, is invalid.