  An extension of the Standard Model by three singlet fermions with masses
smaller than the electroweak scale allows to explain simultaneously neutrino
oscillations, dark matter and baryon asymmetry of the Universe. We discuss the
properties of neutral leptons in this model and the ways they can be searched
for in particle physics experiments. We establish, in particular, a lower and
an upper bound on the strength of interaction of neutral leptons coming from
cosmological considerations and from the data on neutrino oscillations. We
analyse the production of neutral leptons in the decays of different mesons and
in $pp$ collisions. We study in detail decays of neutral leptons and establish
a lower bound on their mass coming from existing experimental data and Big Bang
Nucleosynthesis. We argue that the search for a specific missing energy signal
in kaon decays would allow to strengthen considerably the bounds on neutral
fermion couplings and to find or definitely exclude them below the kaon
threshold. To enter into cosmologically interesting parameter range for masses
above kaon mass the dedicated searches similar to CERN PS191 experiment would
be needed with the use of intensive proton beams. We argue that the use of
CNGS, NuMI, T2K or NuTeV beams could allow to search for singlet leptons below
charm in a large portion of the parameter space of the nuMSM. The search of
singlet fermions in the mass interval 2-5 GeV would require a considerable
increase of the intensity of proton accelerators or the detailed analysis of
kinematics of more than 10^{10} B-meson decays.
