The process algebras Timed Mobility (
TiMo) and its extension Permissions, Timers and Mobility ( PerTiMo) were recently proposed to support engineering applications in distributed system design. TiMoprovides a formal framework in which process migration between distinct locations and timing constraints linked to local clocks can be modelled and analysed. This is extended in PerTiMoby associating access permissions to communication to model security aspects of a distributed system. In this paper we develop a new semantic model for TiMousing Rewriting Logic (RL) and strategies, with the aim of providing a foundation for tool support; in particular, strategies are used to capture the locally maximal concurrent step of a TiMospecification which previously required the use of action rules based on negative premises. This RL model is then extended with access permissions in order to develop a new semantic model for PerTiMo. These RL semantical models are formally proved to be sound and complete with respect to the original operational semantics on which they were based. We present examples of how the developed RL models for TiMoand PerTiMocan be implemented within the strategy-based rewriting system Elanand illustrate the range of (behavioural) properties that can be analysed using such a tool.