The notion of regular variation in R$^n$ introduced by Yakymiv [6] is used to study the asymptotic properties of the Radon and dual Radon transform of R$^n$. As a corollary, an $n$-dimensional version of a theorem of Aljančić, Bojanić and Tomić [5] is proved. This corollary complements results of Ostrogorski [8].