In this paper, we firstly investigate synchronisation and passivity in finite time of coupled memristive neural networks (CMNNs) with and without coupling delays. The key contributions of our work lie on two aspects. On the one hand, by designing suitable controllers, several finite-time synchronisation criteria for the CMNNs with and without coupling delays are established. On the other hand, some sufficient conditions for ensuring finite-time passivity of these considered networks are presented. In addition, two numerical examples are provided to guarantee the availability for the acquired results.