We study the location of the eigenvalues of two non self-adjoint operators. The first one is the generator G of a semigroup V (t) = etG, t ≥ 0, of contractions related to the wave equation with dissipative boundary conditions. The spectrum of G in Re z < 0 is formed by isolated eigenvalues with finite multiplicity and the solutions u(t, x) = eλt f (x) with Gf = λf, Re λ < 0, are called asymptotically disappearing. The location of the eigenvalues of G is important for scattering problems. The second operator we deal with is a matrix non self-adjoint operator related to the interior transmission eigenvalues (ITE). The (ITE) are related to the inverse scattering problems for the reconstruction of the form of non convex obstacles by the far filed operator. The location of (ITE) is also crucial for a Weyl formula with remainder for the counting function of complex (ITE). The results for (ITE) are based on a joint work with G. Vodev.