Perceptuomotor functions that support using hand tools can be examined in other manipulation tasks, such as alignment of objects to surfaces. We examined tufted capuchin monkeys’ and chimpanzees’ performance at aligning objects to surfaces while managing one or two spatial relations to do so. We presented six subjects of each species with a single stick to place into a groove, two sticks of equal length to place into two grooves, or two sticks joined as a T to place into a T-shaped groove. Tufted capuchins and chimpanzees performed equivalently on these tasks, aligning the straight stick to within 22.5° of parallel to the groove in approximately half of their attempts to place it, and taking more attempts to place the T stick than two straight sticks. The findings provide strong evidence that tufted capuchins and chimpanzees do not reliably align even one prominent axial feature of an object to a surface, and that managing two concurrent allocentric spatial relations in an alignment problem is significantly more challenging to them than managing two sequential relations. In contrast, humans from 2 years of age display very different perceptuomotor abilities in a similar task: they align sticks to a groove reliably on each attempt, and they readily manage two allocentric spatial relations concurrently. Limitations in aligning objects and in managing two or more relations at a time significantly constrain how nonhuman primates can use hand tools.