  The dimensional reduction of heterotic supergravity with gauge fields
truncated to the Cartan subalgebra exhibits a continuous O(d,d+16;R) global
symmetry, related to the O(d,d+16;Z) T-duality of heterotic strings on a
d-torus. The O(d,d+16;R) symmetry is not present, however, if the supergravity
reduction is done including the full set of E_8 x E_8 or SO(32) gauge fields.
We analyze which duality symmetries are realized to all orders in $\alpha'$ in
the proper effective field theories for the massless string states. We find a
universal O(d,d;R) symmetry, also predicted by double field theory. We confirm
this by giving a novel formulation of the dimensionally reduced supergravity in
terms of O(d,d) multiplets, and we discuss cases of symmetry enhancement.
