  We analyze the iterative structure of unfactorized partonic structure
functions in the large-x limit, and derive all-order expressions for the
leading-logarithmic off-diagonal splitting functions P_gq and P_qg and the
corresponding coefficient functions C_phi,q and C_2,g in Higgs- and gauge-boson
exchange deep-inelastic scattering. The splitting functions are given in terms
of a new function not encountered in perturbative QCD so far, and vanish
maximally in the supersymmetric limit C_A - C_F to 0. The coefficient functions
do not vanish in this limit, and are given by simple expressions in terms of
the above new function and the well-known leading-logarithmic threshold
exponential. Our results also apply to the evolution of fragmentation functions
and semi-inclusive e^+ e^- annihilation.
