This article investigates the fault-tolerant fixed-time cooperative control problem for nonstrict-feedback nonlinear multiagent systems subject to error constraints and input saturation. Fuzzy logic systems are employed to deal with unknown nonlinear dynamics. By using adaptive technique and power integration technique, two barrier-function-based fixed-time control strategies are projected. In the first scheme, a novel adaptive fault-tolerant distributed fixed-time control protocol is developed. Besides, a new real-time compensation mechanism is proposed, where the compensation signal is provided if and only if there exists input saturation. Compared with the mechanisms for always compensating signals in existing results, the proposed real-time compensation mechanism may reduce energy consumption. In the second scheme, an adaptive fault-tolerant priority-based fixed-time control protocol is proposed, which may reduce the computational complexity arising from numerous neighbors’ variables. Both of the proposed two strategies can avoid the singular problem by constructing high-order derivable continuous functions. Besides, the developed control protocols can ensure the errors in MASs are practical fixed-time stable, meanwhile, the error constraints will not be violated in operation. Stability analysis and simulation results illustrate the effectiveness of the proposed strategies.