Asymmetric nuclear matter is studied in the frame of relativistic mean-field theory, using scalarisoscalar σ, vector-isoscalar ω meson together with their selfinteractions, vector-isovector ρ meson with its cross-interaction with ω meson too, and scalar-isovector δ meson as degrees of freedom. The model is used to parameterize the nuclear matter properties results calculated by more fundamental Dirac-Brueckner-Hartree-Fock theory and thus to provide an effective DBHF model applicable also to finite nuclei. Vector ω-ρ cross-interaction seems to be an useful degree of freedom for describing of the asymmetric nuclear matter, mostly due to its impact on density dependence of the symmetry energy.

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