  Duality symmetries are discussed for non-linear gauge theories of (n-1)-th
rank antisymmetric tensor fields in general even dimensions d=2n. When there
are M field strengths and no scalar fields, the duality symmetry groups should
be compact. We find conditions on the Lagrangian required by compact duality
symmetries and show an example of duality invariant non-linear theories. We
also discuss how to enlarge the duality symmetries to non-compact groups by
coupling scalar fields described by non-linear sigma models.
