A perturbative, non-scaling, QCD approach is used to calculate production cross sections for 'naked' heavy flavour states in pp and pp collisions. The basic subprocesses considered, using lowest-order perturbation theory, are: qq → cc and gg → cc (flavour creation), qc → qc and gc → gc (flavour excitation). The dependence of the calculation on various assumptions and parameters is examined. Numerical results are given over large ranges of the c.m. energy and the heavy quark mass. Contrary to intuitive expectation, the flavour-excitation processes may be an important, possibly the dominant, contribution. For the case of charm, the present experimental situation is reviewed, and it is found that our results are compatible with most of the data (mainly upper limits) but are rather difficult to reconcile with the 100-500 μb cross sections inferred by two bubble-chamber groups in the CERN-SPS beam dump experiments. © 1979.