  Recently a gauged two Higgs doublet model, in which the two Higgs doublets
are embedded into the fundamental representation of an extra local $SU(2)_H$
group, is constructed. Both the new gauge bosons $Z^\prime$ and $W^{\prime
(p,m)}$ are electrically neutral. While $Z^\prime$ can be singly produced at
colliders, $W^{\prime (p,m)}$, which is heavier, must be pair produced. We
explore the constraints of $Z^\prime$ using the current Drell-Yan type data
from the Large Hadron Collider. Anticipating optimistically that $Z^\prime$ can
be discovered via the clean Drell-Yan type signals at high luminosity upgrade
of the collider, we explore the detectability of extra heavy fermions in the
model via the two leptons/jets plus missing transverse energy signals from the
exotic decay modes of $Z^\prime$. For the $W^{\prime (p,m)}$ pair production in
a future 100 TeV proton-proton collider, we demonstrate certain kinematical
distributions for the two/four leptons plus missing energy signals have
distinguishable features from the Standard Model background. In addition,
comparisons of these kinematical distributions between the gauged two Higgs
doublet model and the littlest Higgs model with T-parity, the latter of which
can give rise to the same signals with competitive if not larger cross
sections, are also presented.
