Many animals use formalized signals to communicate dominance relationships. In some primates, such as macaques, the function of such signals varies with dominance style. Despotic species produce unidirectional submission signals that have a dual function: in conflict contexts, they signal a willingness to withdraw, whereas in peaceful contexts, they indicate the agreement to subordination. More despotic species produce these calls to a lesser extent than less despotic species. Here, we investigated whether the use of unidirectional submission signals is also related to dominance style in two lemur species and whether signalling subordination stabilizes social relationships at the group level. Ring-tailed lemurs (Lemur catta) exhibit a more despotic dominance hierarchy than Verreaux's sifakas (Propithecus verreauxi). We observed social interactions in 75 dyads of Verreaux's sifakas and 118 dyads of ring-tailed lemurs. Both species used unidirectional submissive calls that have a dual function, potentially suggesting convergent evolution of the function of these signals in independent primate lineages. However, signalling subordination did not stabilize social relationships at the group level in both species. Additionally, subordination occurred more frequently in dyads of the more despotic ring-tailed lemurs than in Verreaux's sifakas, indicating opposite patterns to macaques in the coevolution of social traits with dominance style. This article is part of the theme issue 'The power of sound: unravelling how acoustic communication shapes group dynamics'.