  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.
