  Krivine and Maurey proved in 1981 that every stable Banach space contains
almost isometric copies of $\ell_p$, for some $p\in[1,\infty)$. In 1983,
Raynaud showed that if a Banach space uniformly embeds into a superstable
Banach space, then $X$ must contain an isomorphic copy of $\ell_p$, for some
$p\in[1,\infty)$. In these notes, we show that if a Banach space coarsely
embeds into a superstable Banach space, then $X$ has a spreading model
isomorphic to $\ell_p$, for some $p\in[1,\infty)$. In particular, we obtain
that there exist reflexive Banach spaces which do not coarsely embed into any
superstable Banach space.
