  We construct nearly topological Yang-Mills theories on eight dimensional
manifolds with a special holonomy group. These manifolds are the Joyce manifold
with $Spin(7)$ holonomy and the Calabi-Yau manifold with SU(4) holonomy. An
invariant closed four form $T_{\mu\nu\rho\sigma}$ on the manifold allows us to
define an analogue of the instanton equation, which serves as a topological
gauge fixing condition in BRST formalism. The model on the Joyce manifold is
related to the eight dimensional supersymmetric Yang-Mills theory. Topological
dimensional reduction to four dimensions gives non-abelian Seiberg-Witten
equation.
