In this paper the methods of cut vertices are applied to deeply inelastic electron scattering, single-particle hadron production in e+e- annihilation, multiparticle inclusive production in e+e- annihilation, μ-pair production in hadron-hadron collisions, wide-angle inclusive hadron production in hadron-hadron collisions, and single-particle production in deeply inelastic electron scattering. A generalized Wilson expansion is discussed in detail for two-particle inclusive production in e+e- annihilation. The question of soft and wee partons is discussed and the cancellation of wee partons demonstrated. The relation of cut vertices to the parton model is briefly discussed. © 1979 The American Physical Society.