Abstract Many formalisms use interleaving to model concurrency. To describe some system behaviours appropriately, we need to limit interleaving. For example, in component-based systems, we wish to limit interleaving to force the inputs to a method to arrive together in order. We introduce interface automata with complex actions (IACA), which add complex actions to de Alfaro and Henzinger's interface automata (IA). A complex action is a sequence of actions that may not be interleaved with actions from other components. The composition and refinement operations are more involved in IACA compared to IA, and we must sacrifice associativity of composition. However, we argue that the advantages of having complex actions make it a useful formalism.