Priority is an important approach to the control of concurrent systems. It is often applied to solve the conflict problems in the design of concurrent systems. In this paper, the concept of dynamic priority systems is developed based on bounded P/T systems and the interleaving and the true-concurrency semantics are provided for them respectively. Dynamic priority systems can be used as both modeling tools to build concurrent and distributed systems and semantic foundations to define prioritised operators in programming languages. Finally, the Occam language with a dynamic prioritised operator based on the concept of dynamic priority systems is extended.