We present how Java threads are used to do concurrent coverification. The threads are scheduled with respect to the order of their priorities in the case of different priorities and by using the Round-Robin technique in the case of equal priorities. The system under coverification we are interested in consists eventually of a number of hardware and software modules described by threads at the behavioral level. The coverification process follows the execution path of the global modeled system and it verifies some specification properties during the simulation. We also discuss the case of untimed and timed coverification. An illustrative application on the broadcasting protocol of cache coherence reveals promising results.