We investigated the interaction between object- and space-based attention by measuring activity in early visual cortex. After central cueing, when subjects directed attention to a spatially defined part of an object, activity in early visual areas was enhanced at corresponding retinotopic representations but also at representations of other locations covered by the object. Different from the assumption of automatic attentional "spreading" within an object, however, activity was greater for representations of cued than of uncued locations on the same object. These findings support an interaction of object-based spatial selection with object-independent spatial mechanisms in directing attention. When the target stimulus did not appear at the expected location, we found higher activation in areas representing other locations on the same object than equidistant locations on other objects. Objects, hence, also guide spatial search, and this may account for the behaviorally observed delay in processing parts of an unattended object.