Structure function evolution at next-to-leading order and beyond

Results are presented of two studies addressing the scaling violations of deep-inelastic structure functions. Factorization-scheme independent fits to all ep and mu p data on F_2 are performed at next-to-leading order (NLO), yielding alpha_s(M_Z) = 0.114 +- 0.002_exp (+0.006-0.004)_th . In order to reduce the theoretical error dominated by the renormalization-scale dependence, the next-higher order (NNLO) needs to be included. For the flavour non-singlet sector, it is shown that available calculations provide sufficient information for this purpose at x > 10^-2.Comment: 3 pages LaTeX including 4 eps-figures, uses npb.sty. Talk presented at DIS'99, DESY-Zeuthen, April 1999. To appear in the proceeding