Offspring are selected to demand more resources than what is optimal for their parents to provide, which results in a complex and dynamic interplay during parental care. Parent-offspring communication often involves conspicuous begging by the offspring which triggers a parental response, typically the transfer of food. So begging and parental provisioning reciprocally influence each other and are therefore expected to coevolve. There is indeed empirical evidence for covariation of offspring begging and parental provisioning at the phenotypic level. However, whether this reflects genetic correlations of mean levels of behaviours or a covariation of the slopes of offspring demand and parental supply functions (= behavioural plasticity) is not known. The latter has gone rather unnoticed - despite the obvious dynamics of parent-offspring communication. In this study we measured parental provisioning and begging behaviour at two different hunger levels using canaries (Serinus canaria) as a model species. This enabled us to simultaneously study the plastic responses of the parents and the offspring to changes in offspring need. We first tested whether parent and offspring behaviours covary phenotypically. Then, using a covariance-partitioning approach, we estimated whether the covariance predominantly occurred at a between-nest level (i.e. indicating a fixed strategy) or at a within-nest level (i.e. reflecting a flexible strategy). We found positive phenotypic covariation of offspring begging and parental provisioning, confirming previous evidence. Yet, this phenotypic covariation was mainly driven by a covariance at the within-nest level. That is parental and offspring behaviours covary because of a plastic behavioural co-adjustment, indicating that behavioural plasticity could be a main driver of parent-offspring coadaptation.