Investigating the ability to entrain to auditory stimuli has been a powerful approach to uncovering the comparative rhythm abilities of different animals. While synchrony to regular simple rhythms is well documented, synchrony to complex stimuli, with multiple components at unequal time intervals, is rarer. Several katydid species with simple calls have been shown to achieve synchrony as part of their natural calling interactions in multi-individual choruses. Yet no study so far has demonstrated synchrony in any insect with a complex call. Using natural calling behaviour and playback experiments, we investigated acoustic synchrony and the mechanisms underlying it in the katydid Mecopoda sp. ‘Two-part caller’. This katydid has a complex call consisting of a long trill followed by two or more chirps. We found that individual males synchronized trills and, to a lesser extent, chirps. Further investigation of trill synchrony showed that the timing of trills is modified by external trills but not chirps. Chirp synchrony is modified by external chirps, but also by trills. We suggest a qualitative two-oscillator model underlying synchrony in this species and discuss the implications for the evolution of acoustic synchrony.