Generalizations of a known limit relationship between the Laguerre polynomials and the Hermite polynomials are provided here in terms of Srivastava-Singhal polynomials \(G^{(\alpha)}_n(x,r,\beta,\kappa)\) and the Hermite polynomials. Limit relationships between various other classical orthogonal polynomials are obtained as particular cases of the main results established earlier.