A new approach for microprocessor implementation is introduced for simultaneous control of the attitude and a number of flexure modes, assuming a lumped parameter dynamics model and control actuators mounted on a central rigid body. The switching times of the bang-bang control to be applied are calculated as a function of the current state estimate so as to render the control system performance almost independent of the microprocessor iteration interval. The control law is applicable where the modes are of arbitrarily low frequency so that the current trend of increasing size of spacecraft structures does not impose a limitation. The approach is naturally suited to gas jet actuators, but is also applicable with continuous actuators such as reaction wheels, in which case control torque saturation limits are automatically considered and the effects of bearing stiction reduced by means of the control dither produced during the limit cycle. Attention is restricted at present to control of a single axis, three-axis control with inter-axis coupling requiring a multivariable extension of the principle. At present, initial conditions must be within a certain neighbourhood of the state origin, but developments of the control principle are envisaged which will remove this restriction. Simulation results are presented of a single-axis control with up to three modes and various combinations of frequency.