The visual system groups image elements that belong to an object and segregates them from other objects and the background. Important cues for this grouping process are the Gestalt criteria, and most theories propose that these are applied in parallel across the visual scene. Here, we find that Gestalt grouping can indeed occur in parallel in some situations, but we demonstrate that there are also situations where Gestalt grouping becomes serial. We observe substantial time delays when image elements have to be grouped indirectly through a chain of local groupings. We call this chaining process "incremental grouping" and demonstrate that it can occur for only a single object at a time. We suggest that incremental grouping requires the gradual spread of object-based attention so that eventually all the object's parts become grouped explicitly by an attentional labeling process. Our findings inspire a new incremental grouping theory that relates the parallel, local grouping process to feedforward processing and the serial, incremental grouping process to recurrent processing in the visual cortex. (Contains 2 footnotes and 9 figures.)