  While N-body simulations testify for a cuspy profile of the central region of
the dark matter haloes, observations favor a shallow, cored density profile of
the central region of, at least, some spiral galaxies and dwarf spheroidals. We
show that a central profile, very close to the observed one, inevitably forms
in the center of dark matter haloes if we make a supposition about a moderate
energy relaxation of the system during the halo formation. If we assume the
energy exchange between dark matter particles during the halo collapse to be
not too intensive, the profile is universal: it depends almost not at all on
the properties of the initial perturbation and is very akin, but not identical,
to the Einasto profile with small Einasto index $n\sim 0.5$. We estimate the
size of the 'central core' of the distribution, i.e., the extent of the very
central region with a respectively gentle profile, and show that the cusp
formation is unlikely, even if the dark matter is cold. The obtained profile is
in a good agreement with observational data for, at least, some types of
galaxies, but clearly disagrees with N-body simulations.
