Parton densities and structure functions beyond the next-to-leading order

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We discuss recent results on the evolution of unpolarized parton densities and structure functions in massless perturbative QCD. Present partial results on the next-to-next-to-leading order (NNLO) evolution kernels prove sufficient for reliable calculations at not too small values of the Bjorken variable, χ > 10 −3. One order more can be taken into account at χ ≥ 0.2. Inclusion of these terms considerably reduces the main theoretical uncertainties of determinations of α s (to about 1% at the Z-mass) and the parton densities from structure functions.