Abstract.We propose an abstract notion of an assembly theory that formalizes rudimentary requirements for systems of interacting components. Among these are a composition operator for assemblies, a communication-safety predicate to express the absence of communication errors, a refinement relation for assemblies, and a packing operation to encapsulate assemblies into components thus allowing hierarchical system constructions. We establish laws that must be satisfied by any concrete assembly theory in order to support compositionality of communication-safety, of encapsulation and of refinement. Moreover, refinement must behave well w.r.t. communication-safety and encapsulation. As a concrete instance we investigate a modal assembly theory using modal I/O-interfaces (MIOs) for modeling observable component behaviors and MIOs with possible error states (indicating communication errors) for modeling assembly behaviors. We show that all rules of an assembly theory are satisfied by modal assemblies, in particular the compositionality requirements hold.