[en] Recently, several ultraluminous X-ray (ULX) sources were shown to host a neutron star (NS) accretor. We perform a suite of evolutionary calculations, which show that, in fact, NSs are the dominant type of ULX accretor. Although black holes (BH) dominate early epochs after the star-formation burst, NSs outweigh them after a few 100 Myr and may appear as late as a few gigayears after the end of the star-formation episode. If star formation is a prolonged and continuous event (i.e., not a relatively short burst), NS accretors dominate the ULX population at any time in the solar metallicity environment, whereas BH accretors dominate when the metallicity is sub-solar. Our results show a very clear (and testable) relation between the companion/donor evolutionary stage and the age of the system. A typical NSULX consists of a $\sim <!--\; ???\; -->1.3M_{\odot <!--\; ???\; -->}$ NS and $\sim <!--\; ???\; -->1.0M_{\odot <!--\; ???\; -->}$ Red Giant. A typical BH ULX consists of a $\sim <!--\; ???\; -->8M_{\odot <!--\; ???\; -->}$ BH and $\sim <!--\; ???\; -->6M_{\odot <!--\; ???\; -->}$ main-sequence star. Additionally, we find that the very luminous ULXs ($L_X\gtrsim <!--\; ???\; -->{10}^{41}$ erg s⁻¹) are predominantly BH systems ($\sim <!--\; ???\; -->9M_{\odot <!--\; ???\; -->}$) with Hertzsprung-gap donors ($\sim <!--\; ???\; -->2M_{\odot <!--\; ???\; -->}$). Nevertheless, some NSULX systems may also reach extremely high X-ray luminosities (≳10⁴¹ erg s⁻¹).