Functional MRI was used to determine how the constituents of the cortical network subserving dynamic spatial working memory respond to two types of increases in task complexity. Participants mentally maintained the most recent location of either one or three objects as the three objects moved discretely in either a two-or three-dimensional array. Cortical activation in the dorsolateral prefrontal (DLPFC) and the parietal cortex increased as a function of the number of object locations to be maintained and the dimensionality of the display. An analysis of the response characteristics of the individual voxels showed that a large proportion were activated only when both the variables imposed the higher level of demand. A smaller proportion were activated specifically in response to increases in task demand associated with each of the independent variables. A second experiment revealed the same effect of dimensionality in the parietal cortex when the movement of objects was signaled auditorily rather than visually, indicating that the additional representational demands induced by 3-D space are independent of input modality. The comodulation of activation in the prefrontal and parietal areas by the amount of computational demand suggests that the collaboration between areas is a basic feature underlying much of the functionality of spatial working memory. © 2000 Academic Press Dealing with dynamic spatial activity is a ubiquitous element of human behavior. Behaviors as general as navigating in a new city, to as specialized as monitoring airplanes in an air traffic control center, often require the maintenance of spatial representations of varying dimensionality, and the updating of the locations of objects as they move in that space. The underlying space may be two-dimensional, as in the case of navigating in a city in which the constraints are largely specified by relations on a two-dimensional map. Alternatively, the space may be a more demanding threedimensional one, as in the case of air traffic control, which adds the dimension of altitude. The demands imposed by keeping track of the locations of objects may also vary from tracking a single object to tracking multiple objects. Mentally updating the locations of targets, maintaining active representations of those locations and of the space, and coordinating these computations are all component processes in spatial working memory. Demands on the spatial working memory system could be imposed by each of these components and through their interplay during a task.A shared facet of several imaging studies of spatial working memory is that they have used maintenance tasks to identify cortical regions involved in memory for spatial location Courtney et al., 1996;Jonides et al., 1993;Smith et al., 1995). However, maintaining information regarding location is only one of several component processes in spatial working memory. Simple maintenance tasks may not necessarily engage the full range of capabilities of the system and consequently may not sufficiently reveal patte...