<p>This paper investigates the fixed-time synchronization (FTS) and preassigned-time synchronization (PTS) of memristive neural networks (MNNs) with mixed-time delays. Firstly, by applying Lyapunov stability theory, fixed/preassigned-time stability lemmas and inequality techniques, several results for FTS and PTS of MNNs are achieved. Secondly, the FTS and PTS results in this paper offer faster convergence rate and more accurate settling times than asymptotic and finite-time synchronization. Thirdly, the model incorporates state-dependent switching, time-varying and distributed delays, and the time delays do not require differentiability, which leading to the results of this paper are more general. Additionally, unlike feedback control, an event-triggered control (ETC) strategy has been designed that enhances communication resource efficiency and reduces control costs. Finally, the correctness of the results is validated through a data simulation example.</p>