  Recent Chandra observations of nearby galaxies have revealed a number of
ultraluminous X-ray sources (ULXs) with super-Eddington luminosities, away from
the central regions of non-active galaxies. The nature of these sources is
still debated. We argue that a fraction of them could be young, Crab-like
pulsars, the X-ray luminosity of which is powered by rotation. We use the
pulsar birth parameters estimated from radio pulsar data to compute the
steady-state pulsar X-ray luminosity distribution as a function of the star
formation rate (SFR) in the galaxy. We find that ~10% of optically dull
galaxies are expected to have a source with L_x >~ 10^{39} erg/s, while
starbursts galaxies should each have several of these sources. We estimate that
the X-ray luminosity of a few percents of galaxies is dominated by a single
bright pulsar with L_x >~10^{39} erg/s, roughly independently of its SFR. We
discuss observational diagnostics that can help distinguish the young pulsar
population in ULXs.
