A computer system has physical processors supporting virtual addressing. Virtual processors represent multiple execution threads, and logical state of all threads of a virtual processor is stored in a state descriptor field in main memory when the virtual processor is removed from one of the physical processors. Each thread has assigned a thread identifier, which is unique in the respective virtual processor only, and each virtual processor has assigned a unique state descriptor identifier. Address translations for the threads of the multiple virtual processors under their respective thread identifier and state descriptor identifier are stored, and a sequence number is generated when an entry in the translation lookaside buffer is created. The sequence number is stored together with a respective thread identifier, state descriptor identifier, and a valid bit in a respective translation lookaside buffer entry. A determination is made as to whether an address translation is stored in the translation lookaside buffer for a current thread identifier and a current state descriptor identifier by comparing the translation lookaside buffer entries with the entries in the state descriptor/thread array.