A new scheme for the adaptive equalisation of incoherently demodulated signals is presented. In the scheme the output from an envelope detector is fed into a tapped-delay-line filter and simultaneously into a simple phase-estimating circuit. An estimate of the intersymbol interference is obtained and this is then subtracted from an estimate of the signal appearing at the input to the envelope detector to obtain an estimate of the transmitted data. The theoretical basis for the operation of the system is derived, and some results obtained when using the system to equalise time-varying channels are presented.