As one of mobile agent applications, many systems which provide continuous service for users moving on a network have been proposed. In these systems, because a movement of mobile agents is performed after a user movement, users must wait for arrival of mobile agents. To reduce users' waiting time, we propose a fundamental framework for mobile agent systems where an agent can move precedently before a user movement. In our framework, it is assumed that computers are connected on a network and users with rewritable devices move on the network. The framework supports precedent movement of mobile agents based on prediction using movement history of users. Because the prediction may be wrong, the framework also provides the following movement of mobile agents. Moreover, the framework provides a recovery method of mobile agents in service in case that mobile agents disappear due to problems such as their bugs. Because we provide some APIs, via which various functions of our framework are accessed, developers of mobile agent systems can easily use our framework using the APIs. We implemented an experimental agent system using the APIs and confirmed that the framework performed correctly using the experimental system.