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

Existence and compactness theory for ALE scalar-flat K\"ahler surfaces