  Relativistic mean-field (RMF) models have been widely used in the study of
many hadronic frameworks because of several important aspects not always
present in nonrelativistic models, such as intrinsic Lorentz covariance,
automatic inclusion of spin, appropriate saturation mechanism for nuclear
matter, causality and, therefore, no problems related to superluminal speed of
sound. With the aim of identifying the models which best satisfy well known
properties of nuclear matter, we have analyzed $263$ parameterizations of seven
different types of RMF models under three different sets of constraints related
to symmetric nuclear matter, pure neutron matter, symmetry energy, and its
derivatives. One of these (SET1) is formed of the same constraints used in a
recent work [M. Dutra et al., Phys. Rev. C 85, 035201 (2012)] in which we
analyzed $240$ Skyrme parameterizations. The results pointed to $2$ models
consistent with all constraints. By using another set of constraints, namely,
SET2a, formed by the updated versions of the previous one, we found $4$ models
approved simultaneously. Finally, in the third set, named SET2b, in which the
values of the constraints are more restrictive, we found $3$ consistent models.
Another interesting feature of our analysis is that the results change
dramatically if we do not consider the constraint regarding the volume part of
the isospin incompressibility ($K_{\tau,\rm v}$). In this case, we have $35$
approved models in SET2a and $30$ in SET2b.
