  In this letter, we present a formal solution to the non-linear field
equations of ten-dimensional super Yang--Mills theory. It is assembled from
products of linearized superfields which have been introduced as multiparticle
superfields in the context of superstring perturbation theory. Their explicit
form follows recursively from the conformal field theory description of the
gluon multiplet in the pure spinor superstring. Furthermore, superfields of
higher mass dimensions are defined and their equations of motion spelled out.
