  We study the $O(D,D+n)$ generalized metric and the gauge symmetries in the
gauged double field theory (DFT) in view of current algebras and sigma models.
We show that the $O(D,D+n)$ generalized metric in the gauged DFT is consistent
with the heterotic sigma models at the leading order in the
$\alpha'$-corrections. We then study the non-Abelian gauge symmetries and
current algebras of heterotic string theories. We show that the algebras
exhibit the correct diffeomorphism, the $B$-field gauge transformations of the
background fields together with the non-Abelian gauge transformations possibly
with the appropriate local Lorentz transformations.
