There have been few studies on formal approaches to the specification and realization of asynchronous sequential circuits. For synchronous sequential circuits, an algebraic method is proposed as one of such approaches, but it cannot be applied to asynchronous ones directly. This paper describes an algebraic method of specifying the abstract behavior of asynchronous sequential circuits. We select an daisy chain arbiter as an example of them. In the arbiter, state transitions are caused by input changes, and all the modules do not always make state transitions simultaneously. These are main obstacles to specify it in the same way as sychronous sequential circuits. In order to remove them, we modify the meaning of input in specifications and introduce pseudo state transitions so that we can regard all the modules as if they make state transitions simultaneously. This method can be applied to most of the other asynchronous sequential circuits.