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.
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