  We develop a superfield formalism for N=4 superconformal two-dimensional
field theory. A list is presented of minimal free superfields, i.e. of
multiplets containing four bosons and four fermions. We show that the
super-Poincar\'e algebra of the six-dimensional superstring in the light-cone
gauge is essentially equivalent to a local N=4 superconformal symmetry, and
outline the construction of octonionic superconformal field theory.
