  Continuous dual symmetry in electrodynamics, Yang-Mills theory and
gravitation is investigated. Dual invariant which leads to badly nonlinear
motion equations is chosen as a Lagrangian of the pure classical dual nonlinear
electrodynamics. In a natural manner some dual angle which is determined by the
electromagnetic strengths at the point of the time-space appears in the model.
Motion equations may well be interpreted as the equations of the standard
Maxwell theory with source. Alternative interpretation is the quasi-Maxwell
linear theory with magnetic charge. Analogous approach is possible in the
Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion
equations possess the same instanton solutions as the conventional Yang--Mills
equations have. An Abelian two-parameter dual group is found to exist in
Gravitation. Irreducible representations have been obtained: the curvature
tensor was expanded into the sum of twice anti-self-dual and self-dual parts.
Gravitational instantons are defined as (real) solutions to the usual duality
equations. Central-symmetry solutions to these equations are obtained. The
twice anti-self-dual part of the curvature tensor may be used for introduction
of new gravitational equations generalizing Einstein's equations. However, the
theory obtained reduces to the conformal-flat Nordstrom theory.
