Prescribed-time consensus tracking for second-order nonlinear multiagent systems (MASs) with the unknown nonlinear dynamics satisfying a time-varying Lipschitz growth rate is investigated in this article. A time-varying function is introduced as a part of the controller gains, and it plays an important role in overcoming the rapid growth of nonlinear terms and in ensuring that the consensus can be achieved in a preassigned time. An integral sliding-mode control protocol, which forces the system trajectory to move on to the defined sliding manifold at the initial moment, is proposed for solving the prescribed-time consensus tracking problem of leader-following MASs with disturbances. Furthermore, we propose a slightly different control law based on terminal sliding-mode control, and under such a controller, the trajectories of each follower reach the sliding manifold in an arbitrary assigned time T1 , and then in a specified time T2 , the position and velocity tracking errors for all followers converge to 0 at the same time instant. Based on the graph theory, state transformations, and Lyapunov theorem, we prove that the proposed solutions are feasible and, finally, three simulation examples are provided to verify the theoretical results.