We introduce the concept of an algebraic state machine. This is a state transition machine all parts of that are described by algebraic and logical means. This way we base the description of state transition systems exclusively on the concept of algebraic specifications. Also the state of an algebraic state machine is represented by an algebra. In particular, we describe the state spaces of the state machine by algebraic techniques, and the state transitions by special axioms called transition rules. Then we show how known concepts from algebraic specifications can be used to provide a notion of parallel composition with asynchronous interaction for algebraic state machines. As example we introduce a notion of object-oriented component and show how algebraic state machines can formalize such components.