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The compensation of channel nonlinearities in digital radio communication systems is considered. A discrete system with memory, inserted between the source and the modulator, is designed with the aim of providing an equivalent channel with a distortionless linear part and no nonlinearities up to a given order. This design is based on a Volterra series model of the channel and on the theory of pth-order inverse systems. Since the compensator design is based on a mathematical model of the channel, the problem of model identification is considered. A modeling technique is described that uses computer simulation and orthogonal Volterra series. Several examples show the performance of this class of compensators