In this article we summarize the relation between the classically integrable structure of two-dimensional sigma models and global $O(d,d)$ transformations. After giving a brief review of the classical integrability and the doubled formalism, we present a recipe for constructing Lax pairs in the $O(d,d)$-deformed models. The key point in our analysis is to apply the so-called $O(d,d)$(-duality) map involving winding coordinates. As an example we discuss the $O(2,2)$ transformation of the $SU(2)$ WZNW model, corresponding to the marginal $J\bar{J}$ deformation.