In this paper, an output-constrained control algorithm is presented for the consensus control of a class of unknown nonaffine multiagent systems (MASs) with partially unknown control directions. Our contribution includes a step forward beyond the usual consensus stabilization result to show that the outputs of agents remain within user-defined time-varying constraints. To achieve the new results, an error transformation technique is established to generate an equivalent MAS from the original one. Stabilization and consensus of the transformed agent states ensure both the satisfaction of the time-varying constraints and the consensus of the original agent states. Based on the Nussbaum gain technique, the unknown control direction problem is solved. By the Lyapunov synthesis, the asymptotic consensus result and the satisfaction of the output constraints are theoretically proved, along with all the closed-loop signals being bounded. Additionally, the developed consensus controller is distributed since each agent only exchanges information with its neighbors. Finally, simulations on a nonaffine MAS demonstrate the effectiveness of the proposed control scheme.