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Double Field Theory is a manifestly T-duality invariant formulation of stringtheory in which the effective theory at any order of $\alpha'$ is invariantunder global $O(D,D)$ transformations and ought to be invariant under gaugetransformations which receive $\alpha'$-corrections. On the other hand, theeffective theory in the usual $D$-dimensional formulation of string theory ismanifestly gauge invariant and ought to be invariant under T-dualitytransformations which receive $\alpha'$-corrections. We speculate that thecombination of these two constraints may fix both the $2D$-dimensional and the$D$-dimensional effective actions without knowledge of the$\alpha'$-corrections of the gauge and the T-duality transformations.  In this paper, using generalized fluxes, we construct arbitrary$O(D,D)$-invariant actions at orders $\alpha'^0$ and $\alpha'$, and thendimensionally reduce them to the $D$-dimensional spacetime. On the other hand,at these orders, we construct arbitrary covariant $D$-dimensional actions.Constraining the two $D$-dimensional actions to be equal up to non-covariantfield redefinitions, we find that both actions are fixed up to overall factorsand up to field redefinitions.

$O(D,D)$-constraint on $D$-dimensional effective actions