  Let $K$ be a field of characteristic $p>0$. It is proved that the group
$\Aut_{ord}(\CD (L_n))$ of order preserving automorphisms of the ring $\CD
(L_n)$ of differential operators on a Laurent polynomial algebra $L_n:=
K[x_1^{\pm 1}, ..., x_n^{\pm 1}]$ is isomorphic to a skew direct product of
groups $\Zp^n \rtimes \Aut_K(L_n)$ where $\Zp$ is the ring of $p$-adic
integers. Moreover, the group $\Aut_{ord}(\CD (L_n))$ is found explicitly.
Similarly, $\Aut_{ord}(\CDPn)\simeq \Aut_K(P_n)$ where $P_n: =K[x_1, ..., x_n]$
is a polynomial algebra.
