The authors propose to combine adaptive equalisation and differentially coherent reception. An appropriate LMS algorithm is deduced to adapt the equaliser. We determine the optimum equaliser coefficients which minimise the mean-squared error between the input to the threshold detector and the desired symbol. The system of equations to solve is not linear as in the coherent reception. It is of the third order and requires computer calculations. The error probability of the differential detector with and without equaliser is calculated for BPSK. Simulation results are also given.