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It has been pointed out by one of the authors (Shaposhnikov 2008Preprint0804.4542) that in the νMSM (Standard Model extended with three right-handed neutrinos with masses smaller than the electroweak scale), there is a corner in the parameter space where CP-violating resonant oscillations among the two heaviest right-handed neutrinos continue to operate below the freeze-out temperature of sphaleron transitions, leading to a lepton asymmetry which is considerably larger than the baryon asymmetry. Consequently, the lightest right-handed ('sterile') neutrinos, which may serve as dark matter, are generated through an efficient resonant mechanism proposed by Shi and Fuller (1999Phys.Rev.Lett.822832 [astro-ph/9810076]). We re-compute the dark matter relic density and non-eq uilibrium momentum distribution function in this situation with quantum field theoretic methods and, confronting the results with existing astrophysical data, derive bounds on the properties of the lightest right-handed neutrinos. Our spectra can be used as an input for structure formation simulations in warm dark matter cosmologies, for a Lyman-α analysis of the dark matter distribution on small scales, and for studying the properties of haloes of dwarf spheroidal galaxies. © 2008 IOP Publishing Ltd.