Ajax supports the development of rich-client Web applications, by providing primitives for the execution of asynchronous requests and for the dynamic update of the page structure and content. Often, Ajax Web applications consist of a single page whose elements are updated in response to callbacks activated asynchronously by the user or by a server message. These features give rise to new kinds of faults that are hardly revealed by existing Web testing approaches. In this paper, we propose a novel state-based testing approach, specifically designed to exercise Ajax Web applications. The Document Object Model (DOM) of the page manipulated by the Ajax code is abstracted into a state model. Callback executions triggered by asynchronous messages received from the Web server are associated with state transitions. Test cases are derived from the state model based on the notion of semantically interacting events. We evaluate the approach on a case study in terms of fault revealing capability. We also measure the amount of manual interventions involved in constructing and refining the model required by this approach.