We introduce an inheritance concept into a specification method of mobile and real-time systems in order to reuse and refine existing specifications. Reusability by inheritance is emphasized in this paper. We take multiple inheritance to enable to reuse several specifications at a time. An upper specification can be skillfully divided into inherited parts and non-inherited ones. Therefore, a necessary part of the specification can be reused for a lower specification. As an application, the FIPA contract net interaction protocol is specified incrementally by using our method. We have been developing support tools for specifications described using our proposed method.