  We present the basic equations and relations for the relativistic static
spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity
(MDG) which is {\em locally} equivalent to the f(R) theories of gravity and
gives an alternative description of the effects of dark matter and dark energy.
The results for the simplest form of the relativistic equation of state (EOS)
of neutron matter are represented. Our approach overcomes the well-known
difficulties of the physics of SSSS in the f(R) theories of gravity introducing
two novel EOS for cosmological energy-pressure densities and dilaton
energy-pressure densities, as well as proper boundary conditions.
