Nuclear matter properties are calculated in the relativistic mean-held 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 16 MeV and 30 MeV, 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 100 MeV 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 0.014 fm(-3) < <rho>(c) < 0.039 fm(-3) and 0.74 < delta (c) less than or equal to 0.95; for a few parameter sets there is no critical point and the pure neutron matter is predicted to he hound. The maximum mass M-NS of neutron stars is predicted in the range 2.45M(circle dot) less than or equal to M-NS less than or equal to 3.26M(circle dot), the corresponding neutron star radius R-NS is in the range 12.2 km less than or equal to R-NS less than or equal to 15.1 km.