In this paper, we attempt to relate types of change processes that are prevalent in groups to types of models that might be employed to represent these processes. Following McGrath´s analysis of the nature of change processes in groups and teams, we distinguish between development, adaptation, group activity, and learning. We argue that for the case where groups act as activity systems (i.e., attempt to achieve common goals in a co-ordinated manner involving planning and division of labour), the notion of a group process needs to take into account multiple types of causality and requires a holistic formal representation. Minimally, a process needs to be conceived on the level of patterns of sequences, but in many cases discrete event model formalisms might be more appropriate. We then survey various methods for process analysis with the goal to find formalization types that are suitable to model change processes that occur in activity systems. Two types of event-based process analysis are discussed in more depth: the first one works with the view of a process as a sequence pattern, and the second one sees a process as an even more holistic and designed structure: a discrete event model. For both cases, we provide examples for event-based computational methods that proved useful in analyzing typical CSCL log files, such as those resulting from asynchronous interactions (we focus on wikis), the those resulting from synchronous interactions (we focus on chats).