  We consider the discrete Sobolev inner product $$(f,g)_S=\int
f(x)g(x)d\mu+Mf^{(j)}(c)g^{(j)}(c), \quad j\in \mathbb{N}\cup\{0\}, \quad
c\in\mathbb{R}, \quad M>0, $$ where $\mu$ is a classical continuous measure
with support on the real line (Jacobi, Laguerre or Hermite). The orthonormal
polynomials with respect to this Sobolev inner product are eigenfunctions of a
differential operator and obtaining the asymptotic behavior of the
corresponding eigenvalues is the principal goal of this paper.
