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.

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