In composite database systems, global transactions are decomposed by the global transaction manager into several global subtransactions that are executed at the corresponding component database systems. This paper shows that the execution and termination of a global transaction depend on the specified extensional assertions on the local classes as well as on the given kinds of global requests. In some cases, a global transaction is supposed to be successful if exactly one global subtransaction is successfully executed. In other cases, all global subtransactions have to be successful in order to commit the global transaction. We discuss various termination rules for global transactions and thus provide new insights into a complex problem.