Spermatozoa from the sea urchin, Lytechinus pictus, can be demembranated with solutions containing Triton X-100 and 5mM-CaCl2 and reactivated in ATP solutions containing low concentrations (10(-9)M) Of free Ca2+ ion to give symmetrical bending wave movements, even at very low ATP concentrations. At ATP concentrations of 0.01-0.02 mM the reactivated spermatozoa have beat frequencies near 1 Hz, nearly normal bend angles, and wave-lengths about 50% longer than normal. 2. The effects of increased viscosity, obtained by addition of methyl cellulose to the reactivation solutions, on bend angle and beat frequency decrease with decreasing ATP concentration, and become almost undetectable at 0.01 mM ATP. On the other hand, the effect of increased viscosity on wavelength shows relatively little change with ATP concentration, although it is noticeably reduced at 0.01 mM ATP. 3. These observations suggest that the beat frequency at low ATP concentrations is determined by an intrinsic rate-limiting process, in contrast to the viscocity-limited behaviour at high beat frequencies. Quantitative agreement with the experimental results is obtained with a model in which ATP concentration and viscosity each determine the rates of one step in a two-step reaction cycle which determines the beat frequency. 4. Two other models which can qualitatively explain the effects of ATP concentration and viscosity on flagellar beat frequency fail to show quantitative agreement with the experimental results. In one of these models, ATP concentration determines the maximum rate of shear between filaments. In the other, ATP concentration determines a time delay which is required to bring the active moment into phase with the elastic moments which would be expected to dominate the bending resistance at low beat frequencies.