An equaliser algorithm is presented which is suitable for use with a differential detector operating in a time dispersive channel. Although differential detection allows the stringent requirements on frequency stability generally imposed on coherent receivers to be relaxed, its performance is more severely degraded by intersymbol interference. The algorithm described in this paper, which has been derived from previous Bayesian coherent methods, is able to provide reliable performance even after differential detection. Results for the differential equaliser operating in a typical indoor wireless channel are presented and are shown to compare favourably with those of a coherent receiver, using decision feedback equalisation, in the presence of a frequency offset. 12 Pages