  The model of minimal dilatonic gravity (MDG), called also the massive
Branse-Dicke model with $\omega =0$, is an alternative model of gravitation,
which uses one Branse-Dicke gravitation-dilaton field $\Phi$ and offers a
simultaneous explanation of the effects of dark energy (DE) and dark matter
(DM). Here we present an extensive research of non-rotating neutron star models
in MDG with four different realistic equations of state (EOS), which are in
agreement with the latest observational data. The equations describing static
spherically symmetric stars in MDG are solved numerically. The effects
corresponding to DE and DM are clearly seen and discussed.
