This paper proposes a new approach to model deductive object databases. Each object database is described by means of a Datalog language extended with extensional updates, called U-Datalog. Each object can change its state and cooperate with other objects. We introduce an extension of U-Datalog to approach the problem of composition among object databases. It can be used for modular database design and for cooperation among databases. The resulting language has a clear semantics for the evolution of objects and for modeling the transactional behavior of the resulting database. Finally, we describe some architectural issues of the prototype which has been developed.