  We study the relation between high-mass X-ray binary (HMXB) population and
recent star formation history (SFH) for the Small Magellanic Cloud (SMC). Using
archival optical SMC observations, we have approximated the color-magnitude
diagrams of the stellar population by model stellar populations and, in this
way, reconstructed the spatially resolved SFH of the galaxy over the past 100
Myr.We analyze the errors and stability of this method for determining the
recent SFH and show that uncertainties in the models of massive stars at late
evolutionary stages are the main factor that limits its accuracy. By combining
the SFH with the spatial distribution of HMXBs obtained from XMM-Newton
observations, we have derived the dependence of the HMXB number on the time
elapsed since the star formation event. The number of young systems with ages
10 Myr is shown to be smaller than the prediction based on the type-II
supernova rate. The HMXB number reaches its maximum ~20-50 Myr after the star
formation event. This may be attributable, at least partly, to a low luminosity
threshold in the population of X-ray sources studied, Lmin~1e+34 erg/s. Be/X
systems make a dominant contribution to this population, while the contribution
from HMXBs with black holes is relatively small.
