We prove that an $f\in A'$, where $A$ is one of spaces $\Cal E$, $\Cal P$, $\Cal O_c$, $\Cal O_m$, or $\Cal K$, has the quasiasymptotic expansions of the first and second kind and that they are equal to the moment expansion of $f$. Also, Abelian-type results for the Stieltjes and the Laplace transforms of tempered distributions are given.