  Nuclear matter and compact neutron stars are studied in the framework of the
non-linear derivative (NLD) model which accounts for the momentum dependence of
relativistic mean-fields. The generalized form of the energy-momentum tensor is
derived which allows to consider different forms of the regulator functions in
the NLD Lagrangian. The thermodynamic consistency of the NLD model is
demonstrated for arbitrary choice of the regulator functions. The NLD approach
describes the bulk properties of the nuclear matter and compares well with
microscopic calculations and Dirac phenomenology. We further study the high
density domain of the nuclear equation of state (EoS) relevant for the matter
in $\beta$-equilibrium inside neutron stars. It is shown that the low density
constraints imposed on the nuclear EoS and by the momentum dependence of the
Schr\"odinger-equivalent optical potential lead to a maximum mass of the
neutron stars around $M \simeq 2 M_{\odot}$ which accommodates the observed
mass of the J1614-2230 millisecond radio pulsar.
