  Inspired by ideas regarding Hermitian NxN matrix fields obeying a
non-associative algebra, 3-dimensional N=8 SUSic field theories are proposed to
on-shell represent subalgebras of OSp(8|2) and OSp(8|4) groups of SUSY
transformations. They are theories of 8 scalar and 8 spinor fields with Yukawa,
quartic and sextic self-interactions. The actions as their R-symmetry exhibit
only SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphisms. It is argued
that the number of degrees of freedom scale like N^{3/2}. There also exists an
extra S_N permutation symmetry group.
