Research on the relationship between the representation of space and time has produced two contrasting proposals. ATOM posits that space and time are represented via a common magnitude system, suggesting a symmetrical relationship between space and time. According to metaphor theory, however, representations of time depend on representations of space asymmetrically. Previous findings in humans have supported metaphor theory. Here, we investigate the relationship between time and space in a nonverbal species, by testing whether non-human primates show space–time interactions consistent with metaphor theory or with ATOM. We tested two rhesus monkeys and 16 adult humans in a nonverbal task that assessed the influence of an irrelevant dimension (time or space) on a relevant dimension (space or time). In humans, spatial extent had a large effect on time judgments whereas time had a small effect on spatial judgments. In monkeys, both spatial and temporal manipulations showed large bi-directional effects on judgments. In contrast to humans, spatial manipulations in monkeys did not produce a larger effect on temporal judgments than the reverse. Thus, consistent with previous findings, human adults showed asymmetrical space–time interactions that were predicted by metaphor theory. In contrast, monkeys showed patterns that were more consistent with ATOM.