PULSARS-rapidly spinning, highly magnetized neutron stars-are thought to lose their rotational energy through the emission of relativistic particles1,2. As the typical lifetime of a pulsar greatly exceeds that of the remnant of the supernova explosion in which it was born, the relativistic wind from older pulsars should interact directly with the interstellar medium; this can give rise to observable pulsar-wind nebulae3. Here we report the detection by the X-ray satellite Rosat of a different type of nebula, associated with the nearby pulsar PSR1929 + 10. The nebula appears as a linear diffuse X-ray feature in the direction opposite to the pulsar's proper motion. In this case, the pulsar wind appears to be confined by the ram-pressure arising from the high velocity of the pulsar through the interstellar medium, resulting in a trail of relativistic electrons with enhanced emissions of synchrotron radiation. Many such nebulae may exist in the solar neighbourhood, but they will be difficult to detect except in those relatively rare cases where the trails point nearly towards us.