The relaxation (straightening) of flagellar rigor waves, which is known to be induced by micromolar ATP concentrations, was investigated with respect to its dependence on the binding and hydrolysis of ATP. Flagellar rigor waves were formed by the dilution of demembranated, reactivated sea urchin ( Lytechinus pictus) spermatozoa into ATP-free buffer . Relaxation in response to nucleotide was quantitated by measuring G, the mean flagellar bend angle per sperm; this novel assay permitted determination of the rate of relaxation . It was found that (a) the rate of flagellar relaxation induced by 4 x 10 -6 M ATP was inhibited 80% by vanadate concentrations of 3 x 10 -5 M and above; (b) of 16 hydrolyzable and nonhydrolyzable nucleotide di-, tri-, and tetraphosphates tested, only three, each of which was hydrolyzed by the flagellar axonemal ATPase activity (ATP, dATP, and E-ATP), were also capable of effecting relaxation ; (c) several hundred ATP molecules were estimated to be hydrolyzed by each dynein arm in the course of flagellar relaxation ; and (d) the ratio of the rate of relaxation to the rate of ATP hydrolysis, which defines the efficiency of ATP utilization, increased 30-fold as the ATP concentration was raised from 2 x 10 -6 to 9 x 10 -6 M. It is concluded that (a) flagellar relaxation depends on ATP hydrolysis ; (b) because it depends on ATP hydrolysis, flagellar relaxation is an inappropriate model system for investigating the role of ATP binding in the mechanochemical cycle of dynein ; and (c) the efficiency of mechanochemical coupling in flagellar motility is an ATP-dependent phenomenon . A general model of relaxation is proposed based on active microtubule sliding.The relaxation (straightening) of rigor-wave sea urchin sperm flagella is currently favored as a model system for investigating the mechanochemical cycle of flagellar motility (18,19,23,24). This is due to the view that relaxation results from the release of dynein cross-bridges in the flagellar axoneme in response to ATP binding . A number of observations have contributed to this view . Dynein arms were shown to be in the cross-bridged configuration in rigor-wave flagella (11), and this configuration correlated with mechanical indices of flagellar rigidity (10, 11) and stiffness (18). Addition of micromolar concentrations of ATP induced rigor-wave flagella to relax (10). Straightening was accompanied by a 15-fold decrease in flagellar stiffness (18); images of dynein cross-bridges were not reported in relaxed flagella (11). The nonhydrolyzable ATP analogue, adenyl-5'-yl imidodiphosphate (AMP-PNP), was reported to act as a competitive inhibitor of the beat frequency of reactivated sea urchin sperm (19,23) and to effect the relaxation of flagellar rigor waves (23). This and other reports that AMP-PNP also caused the dissociation of dynein arms from isolated outer-doublet microtubules (26), and that relaxation was not blocked (24) (12, 16), were reasonably accommodated by a model that interpreted flagellar relaxation as corresponding to ...