This paper is concerned with finite-time synchronization and finite-time $\mathcal {H}_{\infty }$ synchronization for coupled neural networks with multiple state/derivative couplings. Firstly, several sufficient conditions are developed to guarantee the finite-time synchronization for these two networks by using some inequality techniques. Secondly, based on the Lyapunov functional, finite-time $\mathcal {H}_{\infty }$ synchronization problems for those two networks are respectively tackled. Thirdly, nonchattering controllers are designed to overcome the chattering phenomenon appearing in a finite-time controller with the sign function. Finally, two numerical examples are provided to illustrate the effectiveness and correctness of our results.