We consider a space-time-invariant duality symmetric action for a free
Maxwell field and an SL(2,R) X SO(6,22)-invariant effective action de
scribing a low-energy bosonic sector of the heterotic string compactif
ied on a six-dimensional torus. The manifest Lorentz- and general coor
dinate-invariant formulation of the models is achieved by coupling dua
l gauge fields to an auxiliary vector field from an axionic sector of
the theory.