A data processing system (100) includes a main list (126) of tasks, main scheduling scheme, a starvation list (128) of tasks, and a secondary scheduling scheme. A method identifies tasks in the main list that are potentially-starving tasks and places the potentially-starving tasks in the starvation list. A starvation monitor (130) controls starvation of tasks in the system by determining when to use the secondary scheduling scheme to schedule, for execution on a CPU (132), a highest priority task in the starvation list prior to scheduling, pursuant to the main scheduling scheme, other tasks in the main list. The starvation monitor determines a number of times that a task in the main list is pre-empted, by other tasks in the main list, from being scheduled for execution on the CPU. A counter (131) is incremented each occasion that any task not in the starvation list is executed on the CPU.