  We discuss hidden symmetries of M-theory, its feedback on the construction of
the M-theory effective action, and a response of the effective action when
locality is preserved. In particular, the locality of special symmetries of the
duality-symmetric linearized gravity constraints the index structure of the
dual to graviton field in the same manner as it is required to separate the
levels 0 and 1 generators subalgebra from the infinite-dimensional hidden
symmetry algebra of gravitational theory. This conclusion fails once matter
fields are taken into account and we give arguments for that. We end up
outlining current problems and development perspectives.
