Three proteins from cyanobacteria (KaiA, KaiB, and KaiC) can reconstitute circadian oscillations in vitro. At least three molecular properties oscillate during this reaction, namely rhythmic phosphorylation of KaiC, ATP hydrolytic activity of KaiC, and assembly/disassembly of intermolecular complexes among KaiA, KaiB, and KaiC. We found that the intermolecular associations determine key dynamic properties of this in vitro oscillator. For example, mutations within KaiB that alter the rates of binding of KaiB to KaiC also predictably modulate the period of the oscillator. Moreover, we show that KaiA can bind stably to complexes of KaiB and hyperphosphorylated KaiC. Modeling simulations indicate that the function of this binding of KaiA to the KaiB*KaiC complex is to inactivate KaiA's activity, thereby promoting the dephosphorylation phase of the reaction. Therefore, we report here dynamics of interaction of KaiA and KaiB with KaiC that determine the period and amplitude of this in vitro oscillator.