  The present paper is devoted to the description of local and 2-local
automorphisms on Cayley algebras over an arbitrary field $\mathbb{F}$. Given a
Cayley algebra $\mathcal{C}$ with norm $n$, let $O(\mathcal{C},n)$ be the
corresponding orthogonal group. We prove that the group of all local
automorphisms of $\mathcal{C}$ coincides with the group $\{\varphi\in
O(\mathcal{C},n)\mid \varphi(1)=1\}.$ Further we prove that the behavior of
2-local automorphisms depends on the Cayley algebra being split or division.
Every 2-local automorphism on the split Cayley algebra is an automorphism, i.e.
they form the exceptional Lie group $G_2(\mathbb{F})$ if
$\textrm{char}\mathbb{F}\neq 2,3$. On the other hand, on division Cayley
algebras over a field $\mathbb{F}$, the groups of 2-local automorphisms and
local automorphisms coincide, and they are isomorphic to the group
$\{\varphi\in O(\mathcal{C},n)\mid \varphi(1)=1\}.$
