Component-based design aims at building new software systems from pre-existing components. However in current component platforms, reuse of a component is completed from its signature. Thus nothing can be inferred about the interaction between the reused component and its environment and behavioral mismatch may occur. To express component reuse at a behavioral level, we introduce modal automata and acceptance automata as intuitive formalisms for behavioral interface description. From the expressiveness point of view, these formalisms allow to state some forms of liveness properties. We argue that reusing a component C1, the behavior of which is described by the speciacation S1, in order to realize a global system specified by S amounts to exhibiting a residual specification S/S1 so that any model C2 of S/S1 when composed with C1 constitutes a composite system satisfying S. We define a quotient operation for modal automata and acceptance automata of polynomial complexity (quadratic in the size of the specifications).