  In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic
6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by
Higgs fields, and call Donaldson-Thomas equation, to analytically approach the
Donaldson-Thomas invariants. In this article, we consider the equation on
compact K\"ahler threefolds, and study some of analytic properties of solutions
to them, using analytic methods in higher-dimensional Yang-Mills theory
developed by Nakajima and Tian with some additional arguments concerning an
extra non-linear term coming from the Higgs fields. We prove that a sequence of
solutions to the Donaldson-Thomas equation of a unitary vector bundle over a
compact K\"ahler threefold has a converging subsequence outside a closed subset
whose real 2-dimensional Hausdorff measure is finite, provided that the
L^2-norms of the Higgs fields are uniformly bounded. We also prove an
n/2-compactness theorem of solutions to the equations on compact K\"ahler
threefolds.
