The authors propose to combine linear feedback equalisation and decision feedback demodulation for the equalisation of differentially coherent PSK signalling. By modifying the equaliser output based on the decision feedback demodulation before feeding back, the proposed equaliser can be made to behave like one with a decision feedback structure. Indeed, computer simulation results demonstrate that this equaliser performs much better than existing equalisers, such as linear equalisers for differentially coherent detection. Furthermore its performance is even comparable to that of a decision feedback equaliser with coherent detection.