Object grouping is an effective means for managing the complexity in graphics editing. However, research on collaborative object grouping has not been adequate. In this paper, we contribute a novel collaborative object grouping technique, called CoGroup. CoGroup can achieve maximal combined effects among compatible operations and preserve all users' work in the face of conflict without the overhead of undoing and redoing conflict operations as in existing serialization approaches. CoGroup has been implemented in collaborative word processing (CoWord) and slide authoring (CoPowerPoint) systems and is generally applicable to a range of off-the-shelf commercial graphics applications, particularly CAD/CASE tools.