The dependence of ENSO’s period on its amplitude is examined using a simple delayed oscillator model. This dependence is first calculated in the strongly nonlinear regime by extracting and analyzing unstable periodic orbits from the chaotic attractor of the model. In this regime, the period is found to decrease with increasing amplitude. Next, the dependence of the period on the amplitude is also calculated analytically and numerically in the weakly nonlinear regime by varying the ocean–atmosphere coupling coefficient. In this case, the period increases with the amplitude. The weakly nonlinear result reflects the dependence of the period on the ocean– atmosphere coupling strength rather than the dependence on the amplitude, while the strongly nonlinear result is the robust take-home message here: the period reduces with increasing amplitude.