  Nuclear matter properties are calculated in the relativistic mean field
theory by using a number of different parameter sets. The result shows that the
volume energy $a_1$ and the symmetry energy $J$ are around the acceptable
values 16MeV and 30MeV respectively; the incompressibility $K_0$ is
unacceptably high in the linear model, but assumes reasonable value if
nonlinear terms are included; the density symmetry $L$ is around $100MeV$ for
most parameter sets, and the symmetry incompressibility $K_s$ has positive sign
which is opposite to expectations based on the nonrelativistic model. In almost
all parameter sets there exists a critical point $(\rho_c, \delta_c)$, where
the minimum and the maximum of the equation of state are coincident and the
incompressibility equals zero, falling into ranges
0.014fm$^{-3}<\rho_c<0.039$fm$^{-3}$ and $0.74<\delta_c\le0.95$; for a few
parameter sets there is no critical point and the pure neutron matter is
predicted to be bound. The maximum mass $M_{NS}$ of neutron stars is predicted
in the range 2.45M$_\odot\leq M_{NS}\leq 3.26$M$_\odot$, the corresponding
neutron star radius $R_{NS}$ is in the range 12.2km$\leq R_{NS}\leq 15.1$km.
