In this paper we study some asymptotic properties of the sequence of monic polynomials orthogonal with respect to the measure dµ =x 2 +a x 2 +b e -x 2 dx, where a, b > 0 and a = b.In this way we study the outer relative asymptotic with respect to the classical Hermite polynomials; besides, Mehler-Heine type formulas are analyzed.