  We define a Rohlin property for actions of $Z^{2}$ on UHF algebras and show a
noncommutative Rohlin type theorem. Among those actions with the Rohlin
property, we classify product type actions up to outer conjugacy. In particular
we present two classes of UHF algebras. For UHF algebras in one class, which
includes the CAR algebra, there is one and only one outer conjugacy class of
product type actions and for UHF algebras in the other class, contrary to the
case of actions of $Z$, there are infinitely many outer conjugacy classesof
product type actions.
