We investigate the electromagnetic interaction of a relativistic stellar wind with a planet or a smaller body in orbit around a pulsar. This may be relevant to objects such as PSR B1257+12 and PSR B1620-26 that are expected to hold a planetary system, or to pulsars with suspected asteroids or comets. Most models of pulsar winds predict that, albeit highly relativistic, they are slower than Alfvén waves. In that case, a pair of stationary Alfvén waves, called Alfvén wings (AW), is expected to form on the sides of the planet. The wings expand far into the pulsar's wind and they could be strong sources of radio emissions. The Alfvén wings would cause a significant drift over small bodies such as asteroids and comets.