The binding of heavy meromyosin (HMM), a soluble two-headed fragment of myosin, to F-actin was examined at mu = 0.22 M, 22 degrees C. The actin-HMM association constant was determined by having HMM and subfragment 1 (S-1) compete for sites on F-actin. In these experiments, varying concentrations of S-1 were added to a fixed concentration of HMM and F-actin. F-actin and bound fragments (HMM and S-1) then were sedimented and the concentration of unbound fragments was determined. The data were analyzed using a set of theoretical equations proposed by Hill ((1978) Nature 274, 825-826) that provide a simple way of analyzing the relative binding of one- and two-headed ligands. Using these equations, the actin-HMM association constant was determined to be 3 x 10(9) M-1, while under the same conditions the actin-S-1 association constant is 5 x 10(6) M-1 (determined in preceding paper (Greene, L. E., and Eisenberg, E. (1980) J. Biol, Chem. 255, 543-548)). Therefore, under these conditions, HMM binds 600-fold stronger to actin than does S-1, indicating that both of the HMM heads can bind strongly to actin.