  By considering the 3-3-1 and the left-right symmetric models as low energy
effective theories of the $SU(3)_C\otimes SU(3)_L\otimes SU(3)_R$~(for short
$[SU(3)]^3$) gauge group, alternative versions of these models are found. The
new neutral gauge bosons of the universal 3-3-1 model and its flipped versions
are presented; also, the left-right symmetric model and its flipped variants
are studied. Our analysis shows that there are two flipped versions of the
universal 3-3-1 model, with the particularity that both of them have the same
weak charges. For the left-right symmetric model we also found two flipped
versions; one of them new in the literature which, unlike those of the 3-3-1,
requires a dedicated study of its electroweak properties. For all the models
analyzed, the couplings of the $Z'$ bosons to the standard model fermions are
reported. The explicit form of the null space of the vector boson mass matrix
for an arbitrary Higgs tensor and gauge group is also presented. In the general
framework of the $[SU(3)]^3$ gauge group, and by using the LHC experimental
results and EW precision data, limits on the $Z'$ mass and the mixing angle
between $Z$ and the new gauge bosons $Z'$ are obtained. The general results
call for very small mixing angles in the range $10^{-3}$ radians and $M_{Z'}>$
2.5 TeV.
