If the input information fed into a servo mechanism is only available at discrete intervals, the standard methods of servo design may be inadequate, especially if the interval periods are comparatively large. This paper introduces a method of handling the problem by utilizing cascaded integrators to generate polynomials. The error signals, measured at each interval point, are used to modify the coefficients of the polynomials in such a way that the input information may be more and more correctly handled.Assuming ideal integrators, it is shown that the optimum values of the control parameters of the system satisfy a general law; it is further demonstrated that, for a given interval period and number of integrators, the theoretical errors at each interval point can be calculated for any continuous analytical or tabulated input function. The problem of unequal interval periods is also briefly considered.Tests on a Meccano model and large-scale differential analyser have confirmed the theory and indicated that the effect of inaccuracies in instruments are appreciably reduced by the correction system. The arrangement is also shown to be a very effective rate-measuring device—a property which may be of value in certain process-control systems.Some ideas on the problems involved in designing a pulse-monitored servo system are considered, and a brief description is given of an electrical 2-integrator pilot model which has been constructed. It is stressed that the development of such systems is in an early stage, and some of the problems to be tackled in the future are therefore outlined.