Relative motion information, especially relative speed between different input patterns, is required for solving many complex tasks of the visual system, such as depth perception by motion parallax and motion-induced figure/ground segmentation. However, little is known about the neural substrate for processing relative speed information. To explore the neural mechanisms for relative speed, we recorded single-unit responses to relative motion in the primary visual cortex (area V1) of rhesus monkeys while presenting sets of random-dot arrays moving at different speeds. We found that most V1 neurons were sensitive to the existence of a discontinuity in speed, that is, they showed higher responses when relative motion was presented compared to homogenous field motion. Seventy percent of the neurons in our sample responded predominantly to relative rather than to absolute speed. Relative speed tuning curves were similar at different center–surround velocity combinations. These relative motion-sensitive neurons in macaque area V1 probably contribute to figure/ground segmentation and motion discontinuity detection.