Integrable structures in classical off-shell 10D supersymmetric Yang-Millstheory

The field equations of supersymmetric Yang-Mills theory in,ten dimensions m ay be formulated as vanishing curvature conditions on light-like rays in su perspace. In this article, we investigate the physical content of the modif ied SO(7) covariant superspace constraints put forward earlier [11]. To thi s end, group-algebraic methods are developed which allow to derive the set of physical fields and their equations of motion from the superfield expans ion of the supercurl, systematically. A set of integrable superspace constraints is identified which drastically reduces the field content of the unconstrained superfield but leaves the sp ectrum including the original Yang-Mills vector field completely off-shell. A weaker set of constraints gives rise to additional fields obeying first order differential equations. Geometrically, the SO(7) covariant superspace constraints descend from a truncation of Witten's original linear system t o particular one-parameter families of light-like rays.