A privilege level re-mapping mechanism is provided to a processor to re-map privilege levels. The re-mapping mechanism is placed in between the control registers and the privilege checking circuitry, to enable the re-mapping to be dynamically performed in real time prior to privilege checking. The novel dynamic re-mapping of privilege levels prior to privilege checking enables tasks to be executed with relative privilege level relationships that are different from what were nominally assigned to the tasks. In one embodiment, complementary selection mechanism is also provided to enable the novel dynamic re-mapping to be conditionally performed.