  We study the next-to-next-to-leading order (NNLO) evolution of flavour
singlet parton densities and structure functions in massless perturbative QCD.
Present information on the corresponding three-loop splitting functions is used
to derive parametrizations of these quantities, including Bjorken-x dependent
estimates of their residual uncertainties. Compact expressions are also
provided for the exactly known, but in part rather lengthy two-loop singlet
coefficient functions. The size of the NNLO corrections and their effect on the
stability under variations of the renormalization and mass-factorizations
scales are investigated. Except for rather low values of the scales, the
residual uncertainty of the three-loop splitting functions does not lead to
relevant effects for x > 10^-3. Inclusion of the NNLO contributions
considerably reduces the theoretical uncertainty of determinations of the quark
and gluon densities from deep-inelastic structure functions.
