<p>This paper investigates the problem of achieving both fixed-time and predefined-time bipartite consensus tracking (BCT) for second-order nonlinear multi-agent systems (MASs) operating under directed signed topologies. To address the challenges posed by unknown nonlinear dynamics and external disturbances, radial basis function neural networks (RBFNNs) are utilized to approximate the uncertain nonlinearities. For fixed-time BCT, a nonsingular sliding-mode control law is developed, employing a tanh-based sliding surface that ensures smooth control, mitigates chattering, and provides a parameter-independent upper bound on the settling time. Building upon this framework, a predefined-time control protocol is proposed by integrating RBFNNs-based compensation with a segmented nonsingular sliding-mode design, guaranteeing convergence within a predefined time. Finally, simulations are conducted to demonstrate the effectiveness of the proposed control strategies, and the results confirm the superior performance and robustness of the adaptive control approach introduced in this study.</p>