  We consider a class of $2+D$ - dimensional string backgrounds with a target
space metric having a covariantly constant null Killing vector and flat
`transverse' part. The corresponding sigma models are invariant under $D$
abelian isometries and are transformed by $O(D,D)$ duality into models
belonging to the same class. The leading-order solutions of the conformal
invariance equations (metric, antisymmetric tensor and dilaton), as well as the
action of $O(D,D)$ duality transformations on them, are exact, i.e. are not
modified by $\a'$-corrections. This makes a discussion of different space-time
representations of the same string solution (related by $O(D,D|Z)$ duality
subgroup) rather explicit. We show that the $O(D,D)$ duality may connect curved
$2+D$-dimensional backgrounds with solutions having flat metric but, in
general, non-trivial antisymmetric tensor and dilaton. We discuss several
particular examples including the $2+D=4$ - dimensional background that was
recently interpreted in terms of a WZW model.
