The framework of action calculi accommodates a variety of disciplines of interaction and computation. A general theory of action calculi is under development; each particular action calculus — such as the π-calculus — will possess also a specific theory. It has previously been shown that any action calculus can be extended in a conservative manner to higher-order, thus allowing its actions to be encapsulated and treated as data. The dynamics of each higher-order calculus includes β-reduction, analogous to the λ-calculus. This paper demonstrates that under an assumption on the arities of a higher-order calculus (analogous to the assumption of simple types in the λ-calculus), β-reduction in higher-order action calculi is strongly normalising.