This article addresses the distributed containment control problem of nonlinear multiagent systems with directed jointly connected switching topologies. It is assumed that the dynamics of agents are unknown nonlinear pure-feedback forms. The novel adaptive containment-control laws are designed to solve the case without considering the formation among leaders first and then the case of leaders’ formation. Different from the existing results, a condition of average dwell time is given by using the smooth parameter projection. Uniformly ultimate boundedness of the closed-loop system is analyzed in detail. Simulations show the feasibility and effectiveness of the proposed scheme.