An investigation is conducted of two protocols belonging to the priority inheritance protocols class; the two are called the basic priority inheritance protocol and the priority ceiling protocol. Both protocols solve the uncontrolled priority inversion problem. The priority ceiling protocol solves this uncontrolled priority inversion problem particularly well; it reduces the worst-case task-blocking time to at most the duration of execution of a single critical section of a lower-priority task. This protocol also prevents the formation of deadlocks. Sufficient conditions under which a set of periodic tasks using this protocol may be scheduled is derived.