An in vitro motility assay has been developed in which single actin filaments move on one or a few heavy meromyosin (HMM) molecules. This movement is slower than when many HMM molecules are involved, in contrast to analogous experiments with microtubules and kinesin. Frequency analysis shows that sliding speeds distribute around integral multiples of a unitary velocity. This discreteness may be due to differences in the numbers of HMM molecules interacting with each actin filament, where the unitary velocity reflects the activity of one HMM molecule. The value of the unitary velocity predicts a step size of 5-20 nm per ATP, which is consistent with the conventional swinging crossbridge model for myosin function.