  In this paper which is based on the results obtained in collaboration with
Igor Bandos and Dmitri Sorokin I present the extention of the "doubled fields"
formalism by Cremmer, Julia, Lu and Pope to the supersymmetric case and lifting
this construction onto the level of the proper duality-symmetric action for
D=11 supergravity. Further extension of the doubled field formulation to
include dynamical sources is also discussed.
