  Employing hybrid population synthesis, a model of the population of
ultraluminous X-ray sources (ULX) in the binary systems with a black hole (BH)
accretors is computed. It is compared to the model of the population of ULX
with magnetized neutron stars (NS) that can be observed as pulsating ULX
(Kuranov et al. 2020). A model of formation of BH is considered, in which their
mass is determined by the mass of stellar CO core immediately before the
collapse, as well as "delayed" and "rapid" collapse models (Fryer et al. 2012).
Possible transiency of ULX due to accretion disks instability is taken into
account The parameters and evolution of ULX are computed for the galaxies with
constant star formation rate (SFR) and for the ones formed by an instantaneous
star formation burst. The maximum number of ULX with BH ($\sim 10$) is reached
in the galaxies with stationary $ SFR=10$\msun/yr in $\sim 1$ Gyr after
beginning of star formation. ULX which are observed after the end of star
formation, are binaries, in which BH and/or NS formed before the completion of
star formation, while long-living donors with the mass $\sim$\msun\ continue
RLOF or even fill their Roche lobes later. In several Gyr after completion of
star formation the number of ULX in the galaxies with mass
$M_G=10^{10}$\,\msun\ becomes less than 1 per 10 galaxies, most of them are ULX
with NS. In ULX with NS, regardless of the adopted SFR model, dominate
persistent sources with the donor overflowing Roche lobe. The number of
transient sources is by more than an order of magnitude lower. Wind-accreting
ULX are by an order of magnitude more rare than the sources with accretion via
RLOF.
