The problem of extending the language of statecharts to include overlapping states is considered. The need for such an extension is motivated and the subtlety of the problem is illustrated by exhibiting the shortcomings of naive approaches. The syntax and formal semantics of our extension are then presented, showing in the process that the definitions for conventional statecharts constitute a special case. Our definitions are rather complex, a fact that we feel points to the inherent difficulty of such an extension. We thus prefer to leave open the question of whether or not it should be adopted in practice.