  In [arXiv:0808.1677] 3 dimensional field theories are proposed to on-shell
represent N=8 SUSY algebra and SO(7) or SO(4)xSO(4) subgroups of full SO(8)
automorphism. They are theories of 8 scalar and 8 spinor matrix fields with
Yukawa, quartic and sextic self-interactions. This note is devoted to
superfield and off-shell formulation of the theory. Scalar superfields are
proposed to represent scalar supermultiplets. A renormalizable action with
quadratic and quartic self-interactions is proposed to govern their dynamics.
