  Our main result in this article is a compactness result which states that a
noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat
K\"ahler metrics on a minimal K\"ahler surface whose K\"ahler classes stay in a
compact subset of the interior of the K\"ahler cone must have a convergent
subsequence. As an application, we prove the existence of global moduli spaces
of scalar-flat K\"ahler ALE metrics for several infinite families of K\"ahler
ALE spaces.
