Abstract: Methods and systems for process rollback in a shared memory parallel processor computing environment use priority values to control process rollback. Process classes are defined and each process class is allocated a base priority value. Each process run by the system is associated with one of the classes. In accordance with a first embodiment, process priorities determine which process is rolled back. In accordance with a second embodiment, collision counts and class pair priorities determine which process is rolled back. The methods and systems ensure that critical processes are granted at least a minimum allocation of processor time, while less critical processes are not completely starved. The functionality the system is thereby improved.