The purpose of this paper is to compare, in the special subspaces $\mathcal A\{x^{\alpha_n}\}$ of the space of tempered distributions, the notions of the generalized asymptotic expansion introduced by R. Estrado and R. P. Kanwal [1, 2, 3], and the quasiasymptotic expansion of the first and second type at oo introduced by S. Pilipović [4].