SUMMARYA dual-mode multi-modulus algorithm (DM-MMA) and a stop-and-go dual-mode multi-modulus algorithm (SAG-DMMMA) for blind equalisation of high-order quadrature amplitude modulation (QAM) signals are proposed. Simulation results show the proposed blind equalisation algorithms have faster convergence speed and smaller steady-state mean square error, compared with the recently introduced multi-modulus algorithm.