This paper studies the practical fixed-time consensus (Fd-TC) for uncertain multi-agent systems (MASs) under strongly connected directed graphs utilizing adaptive event/self-triggered controllers, respectively. Considering the uncertainty in the agent’s nonlinear dynamic parameters, the adaptive event-triggered controller is designed by incorporating an event-triggered strategy with an adaptive control scheme, which achieves the practical Fd-TC for uncertain nonlinear MASs and the settling time remains constant irrespective of the initial conditions. Moreover, the designed controller is independent of any global information, including communication topology and network size. It also employs the hyperbolic tangent function to tackle Zeno and nondifferential issue. Following this, the adaptive event-triggered controller serves as the foundation for introducing a self-triggered controller, which eliminates the necessity for continuous monitoring and guarantees practical Fd-TC. Furthermore, the results are extended to a more generalized case with uncertain disturbances, highlighting the adaptability of the designed controller. Finally, two numerical simulation examples are conducted to validate the efficacy of the developed controllers.