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In this paper we consider sequences of polynomials orthogonal with respect tocertain discrete Laguerre-Sobolev inner product, with two perturbations(involving derivatives) located inside the oscillatory region for the classicalLaguerre polynomials. We focus our attention on the representation of thesepolynomials in terms of the classical Laguerre polynomials and deduce thecoefficients of their corresponding five-term recurrence relation, as well asthe asymptotic behavior of these coefficients when the degree of thepolynomials tends to infinity. Also, the outer relative asymptotics oforthogonal polynomials with respect to this discrete Sobolev inner product isanalyzed.

Asymptotics for Laguerre-Sobolev type ortogonal polynomials modified within their oscillatory regime