In the present paper we deal with the polynomials L n ( α , M , N ) (x) orthogonal with respect to the Sobolev inner product (p,q) = 1 (α+1)∫0~p(x)q(x)x α e - x dx + Mp(O)q(O) + Np'(O)q'(O), N, M >= O, α > -I , firstly introduced by Koekoek and Meijer in 1993 and extensively studied in the last years. We present some new asymptotic properties of these polynomials and also a limit relation between the zeros of these polynomials and the zeros of Bessel function J α (x). The results are illustrated with numerical examples. Also, some general asymptotic formulas for generalizations of these polynomials are conjectured.