Direct measurements of the stiffness (elastic bending resistance) of demembranated sera urchin sperm flagella were made in the presence of MgATP2- and vanadate. Under these conditions, the flagellum is in a relaxed state, with a stiffness of approximately 0.9 x 10(-21) N m2, which is approximately 5% of the stiffness obtained in the rigor state in the absence of MgATP2-. MgADP- dose not substitute for MgATP2- in producing relaxed state. A progressive inhibition of movement is observed after addition of MgATP2- to flagella preincubated with vanadate, in which new bend generation, propagation, and relaxation by straightening are distinguished, depending on the ratio of MgATP2- and vanadate. At appropriate concentrations of vanadate, increase of the velocity of bend propagation is observed at a very low concentration of MgATP2- that is not enough to induce spontaneous beating. Vanadate enhances competitive inhibition of beat frequency by MgADP- but not by ADP3-, ATP4-, or Pi. These observations, and the uncompetitive inhibition of beat frequency by vanadate, indicate that vanadate can only bind to dynein-nucleotide complexes induced by MgATP2- and MgADP-. The state accessible by MgATP2- binding must be a state in which the cross-bridges are detached and the flagellum is relaxed. The state accessible by MgADP- binding must be a cross-bridged state. Bound vanadate prevents the transition between these two states. Inhibition and relaxation by banadate in the presence of MgATP2- results from the specific affinity of vanadate for a state in which nucleotide is bound, rather than a specific affinity for the deteched state.