  We consider a space-time invariant duality symmetric action for a free
Maxwell field and an $SL(2,{\bf R})\times SO(6,22)$ invariant effective action
describing a low-energy bosonic sector of the heterotic string compactified on
a six-dimensional torus. The manifest Lorentz and general coordinate invariant
formulation of the models is achieved by coupling dual gauge fields to an
auxiliary vector field from an axionic sector of the theory.
