  Let $^*\mathbb{R}$ be a nonstandard extension of $\mathbb{R}$ and $\rho$ be a
positive infinitesimal in $^*\mathbb{R}$. We show how to create a variety of
isomorphisms between A. Robinson's field of asymptotic numbers
$^\rho\mathbb{R}$ and the Hahn field $\hat{^\rho\mathbb{R}}(t^\mathbb{R})$,
where $\hat{^\rho\mathbb{R}}$ is the residue class field of $^\rho\mathbb{R}$.
Then, assuming that $^*\mathbb{R}$ is fully saturated we show that
$\hat{^\rho\mathbb{R}}$ is isomorphic to $^*\mathbb{R}$ and so
$^\rho\mathbb{R}$ contains a copy of $^*\mathbb{R}$. As a consequence (that is
important for applications in non-linear theory of generalized functions) we
show that every two fields of asymptotic numbers corresponding to different
scales are isomorphic.
