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In this paper, we study a delayed HIV infection model with nonmonotonic immune response and perform stability and bifurcation analysis. Our results show that the delayed HIV infection system with nonmonotonic immune response has bistability and stable periodic solution appear. We find that both the uninfected and immune-free equilibria are globally asymptotically stable under certain conditions which are not affected by time delay. However, the time delay makes one immune equilibrium always unstable for τ ≥ 0 and also makes another immune equilibrium appear stability switches; meanwhile, the system will exhibit local Hopf bifurcation, global Hopf bifurcation, and saddle-node-Hopf bifurcation. Numerical simulations are carried out to verify our results. [ABSTRACT FROM AUTHOR]