  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
Alfv\'en waves. In that case, a pair of stationary Alfv\'en waves, called
Alfv\'en 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 Alfv\'en wings would cause a significant drift over small bodies
such as asteroids and comets.
