The aim of a Software Transactional Memory (STM) is to discharge the programmers from the management of synchronization in multiprocess programs that access concurrent objects. To that end, a STM system provides the programmer with the concept of a transaction. The job of the programmer is to decompose each sequential process the application is made up of into transactions. A transaction is a piece of code that accesses concurrent objects, but contains no explicit synchronization statement. It is the job of the underlying STM system to provide the illusion that each transaction appears as being executed atomically. For efficiency, a STM system allows transactions to execute concurrently. Consequently, due to the underlying STM concurrency management, a transaction commits or aborts. This paper first presents a new STM consistency condition, called virtual world consistency. This condition states that no transaction reads object values from an inconsistent global state. It is similar to opacity for the committed transactions but weaker for the aborted transactions. More precisely, it states that (1) the committed transactions can be totally ordered, and (2) the values read by each aborted transaction are consistent with respect to its causal past only. Hence, virtual world consistency is weaker than opacity while keeping its spirit. Then, assuming the objects shared by the processes are atomic read/write objects, the paper presents a STM protocol that ensures virtual world consistency (while guaranteeing the invisibility of the read operations). From an operational point of view, this protocol is based on a vector-clock mechanism. Finally, the paper considers the case where the shared objects are regular read/write objects. It also shows how the protocol can be weakened to satisfy the causal consistency condition (that is weaker than virtual world consistency). Virtual world consistency does not require the aborted transactions to agree on what they have seen. This is captured by the local vector clocks associated with each process and the vector timestamps associated with each object. From a comprehensive point of view, the paper addresses how the interplay of these local control informations allows the execution of a set of transactions to be provided with a global meaning.