  We consider Yang-Mills theory on manifolds ${\mathbb R}\times X$ with a
$d$-dimensional Riemannian manifold $X$ of special holonomy admitting gauge
instanton equations. Instantons are considered as particle-like solutions in
$d+1$ dimensions whose static configurations are concentrated on $X$. We study
how they evolve in time when considered as solutions of the Yang-Millsequations
on ${\mathbb R}\times X$ with moduli depending on time $t\in{\mathbb R}$. It is
shown that in the adiabatic limit, when the metric in the $X$ direction is
scaled down, the classical dynamics of slowly moving instantons corresponds to
a geodesic motion in the moduli space $\cal M$ of gauge instantons on $X$.
Similar results about geodesic motion in the moduli space of monopoles and
vortices in higher dimensions are briefly discussed.
