  We apply the techniques of $S^7$-algebras to the construction of N=5-8
superconformal algebras and of S{\bf O}(1,9), a modification of SO(1,9) which
commutes with $S^7$-transformations. We discuss the relevance of S{\bf O}(1,9)
for off-shell super-Maxwell theory in D=(1,9).

High Energy Physics - Theory