THEORETICAL UNCERTAINTIES IN THE QCD EVOLUTION OF STRUCTURE FUNCTIONSAND THEIR IMPACT ON ALPHA(S)(M(Z)(2))

The differences are discussed between various next-to-leading order pr escriptions for the QCD evolution of parton densities and structure fu nctions. Their quantitative impact is understood to an accuracy of 0.0 2%. The uncertainties due to the freedom to choose the renormalization and factorization scales are studied. The quantitative consequences o f the different uncertainties on the extraction of the strong coupling constant alpha(s) from scaling violations in deep-inelastic scatterin g are estimated for the kinematic regime accessible at HERA.