In this paper, the network models of coupled delayed memristive neural networks (CDMNNs) without and with delayed coupling are studied respectively. Firstly, according to the definitions of ψ-type stability and ψ -type function, the notion of general decay anti-synchronization (GDAS) is introduced. Secondly, by constructing Lyapunov functional, designing controller and using inequality techniques, the corresponding sufficient conditions that reaching GDAS for CDMNNs with and without delayed coupling are deduced. Thirdly, the validity of the results is proved by proper numerical simulation.