This paper presents two nonsmooth leader-following formation protocols for nonidentical Lipschitz nonlinear multi-agent systems with directed communication network topologies. One protocol is used to achieve finite-time formation for first-order systems, and the other to achieve asymptotic formation for second-order systems. In these protocols, the states of all the agents, including the leader and the followers, are available only locally within their neighborhoods. Some sufficient conditions for reaching formations are derived for nonidentical nonlinear systems satisfying locally Lipschitz conditions. To, prove the stability, a new nonsmooth Lyapunov function is constructed, with stability conditions derived under a nonsmooth analysis framework. The proposed formation protocols are applied to multi-spacecraft systems in deep-space exploration, with numerical simulations demonstrating the effectiveness of the theoretical results. (C) 2015 Elsevier Ltd. All rights reserved.