A microscopic treatment of cumulative phenomena based on perturbative calculations of the corresponding quark diagrams near the threshold is presented. Apart from the real threshold x = A at which 3A - 1 valence quarks become soft, all intermediate thresholds with p < 3A - 1 soft quarks are taken into account. The x-behaviour of the structure function is found to be roughly exponential, governed by an effective coupling constant, which depends on the QCD coupling constant and quark mass. It is shown that the spectator contribution to the cumulative particle production rate involves multiple soft quark interactions with the projectile, whose number grows with cumulativity, and results much less than the direct contribution. Comparison to the experimental deuteron structure function and backward pion production rate on Ta at s = 27.5 GeV leads to different values for the effective coupling constant.