We present the results of population synthesis simulations aimed at exploring the evolution of the 2–10 keV luminosity of X-ray binaries in a young stellar population. The results are applicable to populations of extragalactic X-ray binaries in starburst galaxies and many LINERs. We find that the integrated 2–10 keV luminosity of the simulated population reaches a maximum of about $10^{40}\,{\rm erg~s}^{-1}$ after approximately 20 Myr (for a star-formation rate of 10 M$_{\odot}$ yr$^{-1}$) and remains significant even after the end of star formation and the demise of the luminous OB stars. The results of our simulation are in agreement with recently-derived correlations between the X-ray luminosity starburst galaxies and their star-formation rate. We also find that the cumulative luminosity function is initially fairly flat, in agreement with recent observational results, becoming steeper as the population ages and the high-mass X-ray binaries are succeeded by binaries with progressively lighter donor stars. Using the output of Hydrogen-ionizing far-UV photons from the stellar population, we can plot the track of a “post-starburst” system in the $L_{\rm X}-L_{\rm H\alpha}$ diagram. The system starts off in the starburst locus but quickly evolves to the AGN locus where it lingers for at least 1 Gyr.