We consider the triple differential distribution d Gamma/dE(J)dm(2)(J)d Omega(J) for two-jet events at center of mass energy M, smeared over the end-point region m(2)(J)<<M2, absolute value 2E(J)-M approximately Delta, Lambda(QCD)<<Delta<<M. The leading nonperturbative correction, suppressed by Lambda(QCD)/Delta, is given by the matrix element of a single operator. A similar analysis is performed for three-jet events, and the generalization to any number of jets is discussed. At order Lambda(QCD)/Delta, nonperturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two- and three-jet events.