HW/SW codesign and Reconfigurable Computing are commonly used methodologies for digital systems design. However, no previous work has been carried out in order to define a run-time HW/SW codesign methodology for dynamically reconfigurable architectures. Besides, all previous approaches to reconfigurable computing context scheduling are based on static scheduling techniques. In this paper, we present a runtime HW/SW codesign methodology for discrete event systems using dynamically reconfigurable architectures and a dynamic approach to reconfigurable computing multi-context scheduling. We have applied our methodology to software acceleration, and present the obtained results.