Generalised imitation has often been cited in the behaviour analytic literature as a paradigm case of a higher-order response class. However, its determinants have not been established, When, as is the case in published experimental studies of children's imitative performances to date, the to-be-matched behaviours are actions on objects, many nonimitative processes can result in apparently emergent matching. Such confounding sources of control are minimised when the target behaviours are arbitrary gestures. The present experiments explored the matching of (i) arbitrary actions on novel objects with minimal affordances in 3 infants (9 - 15 months), and (ii) gestures alone in 13 infants (15 - 25 months), and in 20 young children (24 - 42 months). In Experiment 1, the infants' performance of the target actions was measured firstly in response to each of four novel objects (Baseline) and next to the target action (Modelling) on each of these objects. In Experiments 2 and 3, participants' unreinforced responses to target behaviours, and their intermittently-reinforced responses to four behaviours that featured in their trained baseline matching relations, were measured. No evidence of higber-order matching was found; rather, the performances of the infants in Experiments 1 and 2, and of the young children in Experiment 3, could be explained in terms of generalisation of extra-experimentally trained matching repertoires. Infants' bigher-order matching abilities were directly tested in Experiments 4 and 5- Following training of four baseline matching relations, and identification of four target behaviours that the infants failed to match, they were trained to produce the target behaviours in the absence of the corresponding modelled behaviour. Infants' unreinforced responses to the modelled target behaviours, interspersed with modelling of the intermittently reinforced baseline behaviours, were then re-tested. The data showed no evidence of higher-order matching and suggest that infants' higher-order matching abilities, not previously directly tested, have been overestimated in the behaviour analytic literature.