  Based on the structure of the three-dimensional superconformal algebra we
show that every irreducible ${\mathcal N}=6$ three-dimensional superconformal
theory containes exactly one conserved U(1)-symmetry current in the stress
tensor supermultiplet and that superconformal symmetry of every ${\mathcal
N}=7$ superconformal theory is in fact enhanced to ${\mathcal N}=8$. Moreover,
an irreducible ${\cal N}=8$ superconformal theory does not have any global
symmetries. The first observation explains why all known examples of ${\mathcal
N}=6$ superconformal theories have a global abelian symmetry.
