  The solution of the Lax tensor equations in the case
$L_{\alpha\beta\gamma}=-L_{\beta\alpha\gamma}$ was analyzed. The Lax tensors on
the dual metrics were investigated. We classified all two dimensional metrics
having the symmetric Lax tensor $L_{\alpha\beta\gamma}$. The Lax tensors of the
flat space, Rindler system and its dual were found.
