Mode-locked fibre ring lasers can generate picosecond optical pulse widths with MHz repetition rates. Applications in optical imaging, or in experiments with pump-probe lasers, benefit from being able synchronize two lasers at high repetition rates, while retaining the narrow optical pulse widths. We investigate the characteristics of an actively mode-locked fibre ring laser, designed as a slave laser and driven by a commercial Ti:Sapphire laser acting as a master. The master-slave synchronization was stabilized for frequency detuning by matching the cavity lengths, and the dependence of the output pulse width of the slave laser was studied as its cavity was detuned. The increase in pulse width was asymmetric about the ring cavity resonance frequency, a phenomenon that we were able to establish as a consequence of an asymmetry in the detuning range of the higher order cavity modes. We observed that the detuning range decreased linearly with the mode number, an observation that was supported by a theoretical perturbative analysis of cavity locking. © 2019, Springer Nature Switzerland AG.