  This paper follows the previous work on generalized abelian gauge field
theory of higher-order derivatives under rotor model and extends the study to
the most generalized non-abelian case. We find that the rotor mechanism from
the abelian case applies nicely to the non-abelian case under the Lorentz gauge
condition. Under the rotor mechanism, the gauge field transforms as $T_{\mu}^a
\rightarrow \Box^n T_{\mu}^a$. When the order of field derivative is $n=0$,
this restores back to the original Yang-Mills action. Our work gives an
extensive generalization of the Yang-Mills theory with higher-order field
derivatives. We also compute the equation of motion and Noether's current of
the generalized non-abelian gauge field theory. Finally, we study the dynamic
instability issue of the theory by the Ostrogradsky construction and the
analysis of the 00-component of the energy-momentum tensor.
