The mechanism of the rhythmic activity of insect fibrillar muscle is best investigated by a method which eliminates the effect of load parameters. Because of the peculiar properties of this type of muscle, sinusoidal analysis is more convenient than transient analysis; the validity of this method is established by demonstrating that this muscle has no significant discontinuities in its tension/velocity relationship. Small sinusoidal length changes are imposed on the muscle with a high-impedance mechanical drive, and the resulting sinusoidal changes of tension give information about the properties of the resting and active muscle. It is shown that the resting muscle can be represented by a visco-elastic model with a time-constant of 1$\cdot $2 ms. At oscillation frequencies in the range 0 to 55 c/s the stimulated muscle behaves as if there were a time delay of about 7 ms between length changes and tension changes. The muscle has been studied at various lengths, with various frequencies of stimulation and under anoxic conditions. It is not possible to describe its active properties in terms of a simple model; it is suggested instead that an explanation of the effects must be sought in the fine structure of the myofibrils. Oscillatory length changes are not accompanied by synchronous potential changes in the external surface membrane of the muscle fibres.