  In this article we consider the $\alpha$--Euler equations in the exterior of
a small fixed disk of radius $\epsilon$. We assume that the initial potential
vorticity is compactly supported and independent of $\epsilon$, and that the
circulation of the unfiltered velocity on the boundary of the disk does not
depend on $\epsilon$. We prove that the solution of this problem converges, as
$\epsilon \to 0$, to the solution of a modified $\alpha$--Euler equation in the
full plane where an additional Dirac located at the center of the disk is
imposed in the potential vorticity.
