  In this paper we show how the abstract behaviours of higher-order systems can
be modelled as final coalgebras of suitable behavioural functors. These
functors have the challenging peculiarity to be circularly defined with their
own final coalgebra. Our main contribution is a general construction for
defining these functors, solving this circularity which is the essence of
higher-order behaviours. This characterisation is syntax agnostic. To achieve
this property, we shift from term passing to behaviour passing: in the former
higher-order is expressed by passing around syntactic objects (such as terms or
processes) as representations of behaviours whereas the former ditches the
syntactic encoding altogether and works directly with behaviours i.e. semantic
objects. From this perspective, the former can be seen as syntactic
higher-order whereas the later as semantic higher-order.
