We have investigated the steps in the actomyosin ATPase cycle that determine the maximum ATPase rate (Vmax) and the binding between myosin subfragment one (S-1) and actin which occurs when the ATPase activity is close to Vmax. We find that the forward rate constant of the initial ATP hydrolysis (initial Pi burst) is about 5 times faster than the maximum turnover rate of the actin S-1 ATPase. Thus, another step in the cycle must be considerably slower than the forward rate of the initial Pi burst. If this slower step occurs only when S-1 is complexed with actin, as originally predicted by the Lymn-Taylor model, the ATPase activity and the fraction of S-1 bound to actin in the steady state should increase almost in parallel as the actin concentration is increased. As measured by turbidity determined in the stopped-flow apparatus, the fraction of S-1 bound to actin, like the ATPase activity, shows a hyperbolic dependence on actin concentration, approaching 100% asymptotically. However, the actin concentration required so that 50% of the S-1 is bound to actin is about 4 times greater than the actin concentration required for half-maximal ATPase activity. Thus, as previously found at 0 degrees C, at 15 degrees C much of the S-1 is dissociated from actin when the ATPase is close to Vmax, showing that a slow first-order transition which follows the initial Pi burst (the transition from the refractory to the nonrefractory state) must be the slowest step in the ATPase cycle. Stopped-flow studies also reveal that the steady-state turbidity level is reached almost instantaneously after the S-1, actin, and ATP are mixed, regardless of the order of mixing. Thus, the binding between S-1 and actin which is observed in the steady state is due to a rapid equilibrium between S-1--ATP and acto--S-1--ATP which is shifted toward acto-S-1--ATP at high actin concentration. Furthermore, both S-1--ATP and S-1--ADP.Pi (the state occurring immediately after the initial Pi burst) appear to have the same binding constant to actin. Thus, at high actin concentration both S-1--ATP and S-1--ADP.Pi are in rapid equilibrium with their respective actin complexes. Although at very high actin concentration almost complete binding of S-1--ATP and S-1--ADP.Pi to actin occurs, there is no inhibition of the ATPase activity at high actin concentration. This strongly suggests that both the initial Pi burst and the slow rate-limiting transition which follows (the transition from the refractory to the nonrefractory state) occur at about the same rates whether the S-1 is bound to or dissociated from actin. We, therefore, conclude that S-1 does not have to dissociate from actin each time an ATP molecule is hydrolyzed.