A multiple quantum well GaAs/AlGaAs laser with two electrically isolated contacts is passively mode locked in an external cavity at the first through sixth harmonics of the pulse round‐trip frequency of 1.17 GHz to produce pulses shorter than 10 ps. The repetition rate is switched between harmonics by adjusting the gain section current, and large hysteresis between the different repetition rates is observed, with up to four different repetition rates for the same gain current. The results are compared with small and large signal passive mode‐locking theories by considering modifications to the saturated gain recovery between pulses when the laser operates at different harmonics.