The cross-bridge cycle and related kinetic parameters in insect muscles is determined in a skinned fiber system. Small preparations consisting of 2 fibers each are isolated from indirect flight muscles from a giant water bug, Lethocerus Colossicus, and used for experiments. These preparations have stretch activation with the rate constant parameters becoming stable at 5% above the slack length and longer. The preparations are activated in the presence of (mM:) 6 CaEGTA (pCa 4.5), 1 Mg++, 10 NaN3, 10 MOPS (pH 7.00), 15 creatine phosphate, 350 unit/ml kinase, 0.05-5mM MgATP, 0-16mM phosphate, and the ionic strength adjusted to 140mM with K proprionate. The kinetic parameters are assessed by small amplitude (0.25%) length oscillations at varying frequencies (0.25-350Hz), and by following amplitude and phase shift in tension. From these, the complex modulus is determined by the ratio of the stress to the strain in the frequency domain. Exponential processes (B) and (C) are identified in the complex modulus data; process (A) is very small or absent. Process (B) is known as oscillatory work, and is equivalent to delayed tension in step analysis. Process (C) is equivalent to phase 2 of the same. When the MgATP concentration is increased, the rate constants of both processes (B) and (C) increase and saturate. With increasing concentrations of phosphate, the rate constant of processes (B) also increases. The MgATP and phosphate dependence of the rate constants are analyzed in terms of a cross-bridge scheme with 5 states, and the following kinetic parameters are deduced: K1 = 0.7mM-1, k2 = 900s-1, k-2 = 180s-1, K2 = 5, and k3 = 70s-1.(ABSTRACT TRUNCATED AT 250 WORDS)