  This paper is inspired from the nice result of Andrew Hassell on the
eigenfunctions in the stadium billiard. From a classical paper of V. Arnol'd,
we know that quasi-modes are not always close to exact modes. We show that, for
almost all Riemannian metrics on closed surfaces with an elliptic generic
closed geodesic C, there exists exact modes located on C. Related problems in
the integrable case are discussed in several papers of John Toth and Steve
Zelditch.
