  We develop the N=8 superfield description of the Bagger-Lambert-Gustavsson
(BLG) model in its Nambu bracket (NB) realization.
  The basic ingredient is the octet of scalar d=3 N=8 superfields depending
also on the coordinates of a compact three dimensional space M. It is
restricted by the 'superembedding-like' equation, which can be treated as
covariantization of the linearized superembedding equation for supermembrane
(M2-brane) with respect volume preserving diffeomorphisms SDiff3 of M. The
curvatures of SDiff3 connection are expressed through the scalar superfields by
the N=8 superfield generalization of the Chern-Simons equation (super-CS
equation). We show how the dynamical BLG equations appear when studying
consistency of these basic equations.
