THE Vela pulsar, PSR0833-45, is a young (104 yr) nearby neutron star emitting pulsed radiation in radio, optical and γ-ray bands1-5. Soft X-ray imaging by the Einstein6 and Exosat7 observatories has revealed a point-like source, at the position of the pulsar, embedded in a compact nebula ~2 arcmin in diameter, but the search for pulsed X-ray emission has proved difficult. There were claims in 1973 of a positive detection8,9 but subsequent observations have failed to confirm them6,10. Here we report an unambiguous detection, by means of the Rosat satellite11, of pulsed X-ray emission from the Vela pulsar, and thus put this long-standing enigma to rest. The pulsed signal is soft, appearing mainly at energies <1 keV. The Rosat observations resolve the two sources of emission, and show that the point-like emission centred on the pulsar is soft, whereas the emission from the compact nebula is hard. Despite the common prejudice that it is the archetypal young pulsar embedded in a supernova remnant, these observations show that Vela more closely resembles older (105 yr) pulsars.