  We consider the {\it infinite Johnson graph} $J_{\infty}$ whose vertex set
consists of all subsets $X\subset {\mathbb N}$ satisfying $|X|=|{\mathbb
N}\setminus X|=\infty$ and whose edges are pairs of such subsets $X,Y$
satisfying $|X\setminus Y|=|Y\setminus X|=1$. An automorphism of $J_{\infty}$
is said to be {\it regular} if it is induced by a permutation on $\mathbb{N}$
or it is the composition of the automorphism induced by a permutation on
$\mathbb{N}$ and the automorphism $X\to {\mathbb N}\setminus X$. The graph
$J_{\infty}$ admits non-regular automorphisms. Our first result states that the
restriction of every automorphism of $J_{\infty}$ to any connected component
($J_{\infty}$ is not connected) coincides with the restriction of a regular
automorphism. The second result is a characterization of regular automorphisms
of $J_{\infty}$ as order preserving and order reversing bijective
transformations of the vertex set of $J_{\infty}$ (the vertex set is partially
ordered by the inclusion relation). As an application, we describe
automorphisms of the associated {\it infinite Kneser graph}.
