  Model-independent features of hybrid states with heavy quarks and adiabatic
approximation for such systems are discussed.These general arguments are
applied to the QCD-based constituent gluon model.The leading- order Hamiltonian
is derived from the general formalism. The masses of heavy quarks hybrids,
including charmonium hybrid states,are calculated. We predict $c\bar c g$
hybrids at 4.0$\pm$0.1 GeV and $b \bar b g$ ones at 10.5$\pm$0.1 GeV.Comparison
with some other models are made.
