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This paper presents the modal interface theory, a unification of interface automata and modal specifications, two radically dissimilar models for interface theories. Interface automata is a game-based model, which allows the designer to express assumptions on the environment and which uses an optimistic view of composition: two components can be composed if there is an environment where they can work together. Modal specifications are a language theoretic account of a fragment of the modal mu-calculus logic with a rich composition algebra which meets certain methodological requirements but which does not allow the environment and the component to be distinguished. The present paper contributes a more thorough unification of the two theories by correcting a first attempt in this direction by Larsen et al., drawing a complete picture of the modal interface algebra, and pushing the comparison between interface automata, modal automata and modal interfaces even further. The work reported here is based on earlier work presented in [41] and [42].