  We discuss a confining model for charmonium in which the attractive force are
derived from a new type of gauge field equation with a generalized $SU_3$ gauge
symmetry. The new gauge transformations involve non-integrable phase factors
with vector gauge functions $\om^a_{\mu}(x)$. These transformations reduce to
the usual $SU_3$ gauge transformations in the special case $\om^a_\mu(x) =
\p_\mu \xi^a(x)$. Such a generalized gauge symmetry leads to the fourth-order
equations for new gauge fields and to the linear confining potentials. The
fourth-order field equation implies that the corresponding massless gauge boson
has non-definite energy. However, the new gauge boson is permanently confined
in a quark system by the linear potential. We use the empirical potentials of
the Cornell group for charmonium to obtain the coupling strength $f^2/(4\pi)
\approx 0.19$ for the strong interaction. Such a confining model of quark
dynamics could be compatible with perturbation. The model can be applied to
other quark-antiquark systems.
