  Based on the properties of the critical and the actual effective masses of
sigma and omega mesons, criteria to estimate the values of the isoscalar
nonlinear terms of the standard relativistic mean field model that reproduce
stable equations of state in respect to particle hole excitation at high
densities are derived. The relation between nuclear matter stability and the
symmetric nuclear matter properties are shown. The criteria are used to analyze
in a more systematic way the high-density longitudinal and transverse
instabilities of some parameter sets of relativistic mean field models. The
critical role of the vector and vector-scalar nonlinear terms is also discussed
quantitatively.
