  We study analytic aspects of U(n) gauge theory over a toric noncommutative
manifold $M_\theta$. We analyse moduli spaces of solutions to the self-dual
Yang-Mills equations on U(2) vector bundles over four-manifolds $M_\theta$,
showing that each such moduli space is either empty or a smooth Hausdorff
manifold whose dimension we explicitly compute. In the special case of the
four-sphere $S^4_\theta$ we find that the moduli space of U(2) instantons with
fixed second Chern number $k$ is a smooth manifold of dimension $8k-3$.
