  We study the construction of covariant nonlinear duality-symmetric actions in
dual formulation. Essentially, the construction is the PST-covariantisation and
nonlinearisation of Zwanziger action. The covariantisation made use of three
auxiliary scalar fields. Apart from these, the construction proceed in a
similar way to that of the standard formulation. For example, the theories can
be extended to include interactions with external fields, and that the theories
possess two local PST symmetries. We then explicitly demonstrate the
construction of covariant nonlinear duality-symmetric actions in dual
formulation of DBI theory, and D3-brane. For each of these theories, the
twisted self-duality condition obtained from duality-symmetric actions are
explicitly shown to match with the duality relation between field strength and
its dual from the one-potential actions. Their on-shell actions between the
duality-symmetric and the one potential versions are also shown to match. We
also explicitly prove kappa-symmetry of the covariant nonlinear
duality-symmetric D3-brane action in dual formulation.
