We consider locally linear Z_p x Z_p actions on the four-sphere. We present
simple constructions of interesting examples, and then prove that a given
action is concordant to its linear model if and only if a single surgery
obstruction taking to form of an Arf invariant vanishes. We discuss the
behavior of this invariant under various connected-sum operations, and conclude
with a brief discussion of the existence of actions which are not concordant to
their linear models