Although Ada defines a number of mechanisms for specifying scheduling policies, only one, Fifo_Within_Priorities is guaranteed to be supported by all implementations of the Real-Time Systems Annex. Many applications have a mixture of real-time and non real-time activities. The natural way of scheduling non real-time activities is by time sharing the processor using Round Robin Scheduling. Currently, the only way of achieving this is by incorporating yield operations in the code. This is ad hoc and intrusive. The paper proposes a new scheduling policy which allows one or more priority levels to be identified as round robin priorities. A task whose base priority is set to one of these levels is scheduled in a round robin manner with a user-definable quantum.