The brain directs its limited processing resources through various selection mechanisms, broadly referred to as attention. The present study investigated the temporal dynamics of two such selection mechanisms: space- and object-based selection. Previous evidence has demonstrated that preferential processing resulting from a spatial cue (i.e., space-based selection) spreads to uncued locations if those locations are part of the same object (i.e., resulting in object-based selection), but little is known about the relationship between these fundamental selection mechanisms. Here, we used human behavioral data to determine how space- and object-based selection simultaneously evolve under conditions that promote sustained attention at a cued location, varying the cue-to-target interval from 300 to 1100 ms. We tracked visual-target detection at a cued location (i.e., space-based selection), at an uncued location that was part of the same object (i.e., object-based selection), and at an uncued location that was part of a different object (i.e., in the absence of space- and object-based selection). The data demonstrate that even under static conditions, there is a moment-to-moment reweighting of attentional priorities based on object properties. This reweighting is revealed through rhythmic patterns of visual-target detection both within (at 8 Hz) and between (at 4 Hz) objects.