Density-dependent parametrization models of the nucleon-meson coupling constants,including the isovector scalar δ-field,are applied to asymmetric nuclear matter.The nuclear equation of state (EOS) and the neutron star properties are studied in a relativistic Lagrangian density,using the relativistic mean field (RMF) hadron theory.It is known that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses,finally influences the stability of the neutron stars.We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the 5-field effects in asymmetric nuclear matter.Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the δ-meson in the density-dependent models of the coupling constants.The EOS of nuclear matter strongly depends on the density dependence of the interactions. Density-dependent parametrization models of the nucleon-meson coupling constants, including the isovector scalar δ-field, are applied to asymmetric nuclear matter. The nuclear equation of state (EOS) and the neutron star properties are studied in a relativistic Lagrangian density, using the relativistic mean field (RMF) hadron theory. It is known that the δ-field in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influences the stability of the neutron stars. We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the 5-field effects in asymmetric nuclear matter. Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the δ-meson in the density-dependent models of the coupling constants. The EOS of nuclear matter strongly depends on the density dependence o f the interactions.