  We give a brief review of Bagger-Lambert-Gustavsson (BLG) model, with
emphasis on its version invariant under the volume preserving diffeomorphisms
(SDiff3) symmetry. We describe the on-shell superfield formulation of this
SDiff3 BLG model in standard N=8, d=3 superspace, as well as its superfield
action in the pure spinor N=8 superspace. We also briefly address the
Aharony-Bergman-Jafferis-Maldacena (ABJM/ABJ) model invariant under
$SU(M)_{k}\times SU(N')_{-k}$ gauge symmetry, and discuss the possible form of
their N=6 and, for the case of Chern-Simons level k=1,2, N=8 superfield
equations.
