Model-based testing (MBT) promises a scalable solution to testing large systems, if a model is available. Creating these models for large systems, however, has proven to be difficult. Composing larger models from smaller ones could solve this, but our current MBT conformance relation uioco is not compositional, i.e. correctly tested components, when composed into a system, can still lead to a faulty system. To catch these integration problems, we introduce a new relation over component models called mutual acceptance. Mutually accepting components are guaranteed to communicate correctly, which makes MBT compositional. In addition to providing compositionality, mutual acceptance has benefits when retesting systems with updated components, and when diagnosing systems consisting of components. Keywords: model-based testing • component-based testing • compositional testing • labelled transition systems • uioco This work is part of the project TiCToC -Testing in Times of Continuous Change, project nr 17936, part of the research program MasCot -Mastering Complexity, which is supported by the Dutch Research Council NWO.