This paper focuses on studying containment control problem with switching communication graphs of continuous-time heterogeneous multiagent systems where the control inputs are constrained in a nonconvex set. A nonlinear projection algorithm is proposed to address the problem. We discuss the stability and containment control of the system with switching topologies and nonconvex control input constraints under three different conditions. It is shown that all agents converge to the convex hull of the given leaders ultimately while staying in the nonconvex set (...) under the premise that at least one directed path from leaders to the agents exists in each bounded time interval. Finally, the validity of the results obtained in this paper is verified by simulation. (shrink)