In this paper, we discuss a viewpoint to regard individuals in a society as cognitive agents having internal dynamics, in order to study the dynamic nature of social structures. Internal dynamics is the autonomous changes of an agent's internal states that govern his/her behavior. We first discuss the benefit of introducing internal dynamics into a model of humans and the dynamics of society. Then we propose a simple recurrent network with self-influential connection (SRN-SIC) as a model of an agent with internal dynamics. We report the results of our simulation in which the agents play a minority game. In the simulation, we observe the dynamics of the game as a macro structure itinerating among various dynamical states such as fixed points and periodic motions via aperiodic motions. This itinerant change of the macro structures is shown to be induced by the internal dynamics of the agents.