  A way of covariantizing duality symmetric actions is proposed. As examples
considered are a manifestly space-time invariant duality--symmetric action for
abelian gauge fields coupled to axion-dilaton fields and gravity in D=4, and a
Lorentz-invariant action for chiral bosons in D=2. The latter is shown to admit
a manifestly supersymmetric generalization for describing chiral superfields in
n=(1,0) D=2 superspace.
