  In an extention of the Standard Model by three relatively light right-handed
neutrinos (the nuMSM model) the role of the dark matter particle is played by
the lightest sterile neutrino. We demonstrate that the observations of the
extragalactic X-ray background allow to put a strong upper bound on the mass of
the lightest active neutrino and predict the absolute values of the mass of the
two heavier active neutrinos in the nuMSM, provided that the mass of the dark
matter sterile neutrino is larger than 1.8 keV.
