Synchronisation is widespread in animals, and studies have often emphasised how this seemingly complex phenomenon can emerge from very simple rules. However, the amount of flexibility and control that animals might have over synchronisation properties, such as the strength of coupling, remains underexplored. Here, we studied how pairs of marmoset monkeys coordinated vigilance while feeding. By modelling them as coupled oscillators, we noted that (1) individual marmosets do not show perfect periodicity in vigilance behaviours, (2) even then, pairs of marmosets developed a tendency to take turns being vigilant, a case of anti-phase synchrony, (3) marmosets could couple flexibly; the coupling strength varied with every new joint feeding bout, and (4) marmosets could control the coupling strength; dyads showed increased coupling if they began in a more desynchronised state. Such flexibility and control over synchronisation require more than simple interaction rules. Minimally, animals must estimate the current degree of asynchrony and adjust their behaviour accordingly. Moreover, the fact that each marmoset is inherently non-periodic adds to the cognitive demand. Overall, our study taps into the cognitive aspects of synchronisation and provides a mathematical framework to investigate the phenomenon more widely, where individuals may not display perfectly rhythmic behaviours.