In this work, we investigate an HIV-1 infection model with a general incidence rate and delayed CTL immune response. The model admits three possible equilibria, an infection-free equilibrium E * 0 , CTL-inactivated infection equilibrium E * 1 and CTL-activated infection equilibrium E * 2 . We prove that in the absence of CTL immune delay, the model has exactly the basic behaviour model, for all positive intracellular delays, the global dynamics are determined by two threshold parameters R 0 and R 1 , if R 0 ≤ 1, E * 0 is globally asymptotically stable, if R 1 ≤ 1 < R 0 , E * 1 is globally asymptotically stable and if R 1 >1, E * 2 is globally asymptotically stable. But if the CTL immune response delay is different from zero, then the behaviour of the model at E * 2 changes completely, although R 1 > 1, a Hopf bifurcation at E * 2 is established. In the end, we present some numerical simulations.
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