ESDU 84020 explains the derivation and application of the indicial (step-response) functions (also called Wagner and Kussner functions) used to study aircraft response. The functions are introduced through the Fourier integration of the frequency-dependent generalised airforce coefficients associated with oscillatory motion. Indicial functions for use in predicting response in lift and pitching moment due to heave or pitch rate, or deflection of a 20 per cent chord control, are tabulated for thin aerofoils in subsonic and supersonic flows. Results obtained for a range of typical airframe two- and three-dimensional geometries, including wing/tailplane combinations, again through the speed range to supersonic, are illustrated graphically. They include the effects of active controls. The results are discussed and various aspects of the mathematical modelling of unsteady flows are highlighted.