The problem of effectively scheduling soft tasks whilst guaranteeing the behaviour of hard tasks has been addressed in many papers and a large number of techniques have been proposed. The dual priority mechanism is an intuitively simple method with low overheads. A hard task is assigned two priorities. Upon invocation, the task starts executing with a low priority and it is promoted to a high priority at a time that will guarantee that its deadline is met. Soft tasks are assigned medium priorities; they can thus preempt any hard task that is executing before its promotion time. To increase the capacity for soft tasks, and therefore the effectiveness of the real-time system, hard tasks may be assigned a (/sub m//sup n/)-hard (read n in m) temporal constraint. This implies that the task must meet n deadlines in any m invocations. This paper addresses the combination of such constraints and dual priority scheduling. This approach reduces the gap between dynamic priority and fixed priority scheduling with the goal of reducing the average response time of soft tasks.