The mechanical properties and the activity of the myofibrillar ATPase have been investigated at 21 degrees C on glycerinated back muscle from the water-bug Lethocerus colossicus. When the fibres were held under isometric conditions after stretching them by 0.5--4%, the ATPase required to maintain a given tension increases from 19 to 39 p-moles ATP split for each mg of tension developed as the Ca2+ level is increased from 10(-7) to up to 10(-5) M. The mechanical properties and the ATPase activity have been determined for Ca2+-activated fibres using sinusoidal frequencies of 1--30 HZ and oscillatory amplitudes of 0.5--6% peak-to-peak. In this way the R.M.S. velocity of sinusoidal movement was varied between 0.1-10 mm/sec. The rate of ATP splitting associated with oscillatory tension development, the dynamic tension cost, increases both with Ca2+ and with frequency of oscillation (at 1% peak-to-peak amplitude), becoming as high as four times the isometric value. The oscillatory power output which can be obtained is increased when the Ca2+ level is raised from 10(-7) to 10(-5) M or towards higher amplitudes of oscillation. The chemo-mechanical coupling efficiency increases proportionally with the R.M.S. velocity of muscle movement. In presence of 10(-5) M Ca2+ optimal efficiencies of 5.5--6.2 kcal work per mole ATP split are obtained at R.M.S. velocities of 1.3--2 muscle lengths/sec. The ability of the muscle fibres to perform osciillatory work at the higher frequencies was much reduced at lower Ca2+ levels of 10(-6) or 10(-7) M and the maximal efficiencies never exceeded 2.2 kcal/mole.