  In this paper we analyze the asymptotic behavior of several fractional
eigenvalue problems by means of Gamma-convergence methods. This method allows
us to treat different eigenvalue problems under a unified framework. We are
able to recover some known results for the behavior of the eigenvalues of the
$p-$fractional laplacian when the fractional parameter $s$ goes to 1, and to
extend some known results for the behavior of the same eigenvalue problem when
$p$ goes to $\infty$. Finally we analyze other eigenvalue problems not
previously covered in the literature.
