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In order to characterize jet structure more completely than is possible with the single-hadron fragmentation functions of partons, we deduce the evolution (in Q 2 , equations for the fragmentation functions of a parton to fragment into an arbitrary number N of hadrons. The solution to the evolution equations is explicitly displayed in terms of multiple moments for the N-hadron fragmentation functions. Our procedure is simpler than using the rules of the jet calculus. We also show how the Q dependence of these fragmentation functions can be understood in a recursive cascade-model framework in which both the momentum and the amount by which a parton is off its energy shell (as measured by Q 2, are reduced at each branching step during jet formation. This reformulation suggests an alternative way for solving the evolution equations in which moment inversion is not required.