[en] Perturbative QCD is applied to multiple jet production in e⁺e^-annihilation. We propose modified evolution equations for deriving the all-order perturbative expressions for jet cross sections, defined in the framework of the recently introduced 'k _{perpendicularto} ' clustering algorithm. The mean number of jets as a function of the jet resolution parameter y_cut is studied to relate the effective MLLA scale parameter Λ to Λsub( anti M anti S). Analytical predictions are compared with the results of ARIADNE and JETSET Monte Carlo simulations. (orig.)