We present the concept of mobile groups as a basic mechanism for both the reliable migration and the coordination of mobile processes. Analogously to traditional group systems, mobile groups also provide message delivery guarantees and virtual synchrony. Furthermore, they make process mobility not only visible for the group, but also consistently ordered with other group actions (such as crashes, joins, leaves, and other migrations). The mobile groups approach represents a novel mobility support mechanism which can be used to handle reliability of mobile distributed systems (such as the mobile agent systems), at the application and system level (e.g., for coordinating distributed agents and for reliable agent migration, respectively). In this paper, we discuss the motivations for the mobile groups, formally define their basic properties, and present a membership protocol for such groups. We also discuss some implementation issues and present the advantages of mobile groups against mechanisms commonly employed for the coordination of mobile processes or agents.