  The implementation of seesaw mechanisms to give mass to neutrinos in the
presence of an anomaly-free U(1)_X gauge symmetry is discussed in the context
of minimal extensions of the standard model. It is shown that type-I and
type-III seesaw mechanisms cannot be simultaneously implemented with an
anomaly-free local U(1)_X, unless the symmetry is a replica of the well-known
hypercharge. For combined type-I/II or type-III/II seesaw models it is always
possible to find nontrivial anomaly-free charge assignments, which are however
tightly constrained, if the new neutral gauge boson is kinematically accessible
at LHC. The discovery of the latter and the measurement of its decays into
third-generation quarks, as well as its mixing with the standard Z boson, would
allow one to discriminate among different seesaw realizations.
