Global systems – systems which may operate over transient networks including mobile elements and in which computation itself may be mobile – are gaining in importance. Nevertheless, the means for their modelling are still underdeveloped. The Unified Modelling Language (UML) is well developed for convenient modelling of behavior, but is not yet so useful for modelling aspects of design relevant to global systems, such as mobility. Non-functional requirements such as performance and security also assume an increased importance in the context of global systems, and here too, UML requires enhancement. In this paper we present an extension to UML class, sequence and activity diagrams to model mobile systems. We also describe extensions to model performance and security characteristics. We will describe how, wherever possible, we reuse existing work in these areas.