Contextual influences shape our perception of local visual stimuli. Relative-motion stimuli represent an important contextual influence, yet the mechanism subserving relative-motion computation remains largely unknown. In the present work, we investigated the responses of an established model for simple and complex cells to relative-motion stimuli. A straightforward mathematical analysis showed that relative-motion computation is inherent in the nonlinear transformation of the complex-cell model. Tuning to relative velocity is achieved by applying a temporal filter to the complex-cell response. The mathematical inference is supported by simulations that quantitatively reproduce measured complex-cell responses in both cat and monkey to a variety of relative-motion stimuli. Importantly, the posited mechanism for cortical computation of relative motion does not require an intermediate neural representation of local velocities and does not require lateral or feedback interactions within a network.