In this paper we study the role played both by novae and single stars in enriching the interstellar medium of the Galaxy with CNO group nuclei, in the framework of a detailed successful model for the chemical evolution of both the Galactic halo and disc. First, we consider only the nucleosynthesis from single low-mass, intermediate-mass and massive stars. In particular, the nucleosynthesis prescriptions in the framework of the adopted model are such that (i) low- and intermediate-mass stars are responsible for the production of most of the Galactic C-12 and N-14; (ii) massive stars produce the bulk of the Galactic O-16; (iii) C-13 and O-17 originate mostly in intermediate-mass stars, with only a minor contribution from low-mass and massive stars. In this context, we show that the behaviour of the C-12/C-13, N-14/N-15 and O-16/O-17 isotopic ratios, as inferred from observations, can be explained only allowing for a substantial revision of the available stellar yields. On the other hand, the introduction of nova nucleosynthesis allows us to better explain the temporal evolution of the CNO isotopic ratios in the solar neighbourhood as well as their trends across the Galactic disc. Once all the nucleosynthesis sources of CNO elements are taken into account, we conclude that C-13, N-15 and O-17 are likely to have both a primary and a secondary origin, in contrast to previous beliefs. We show that, when adopting the most recent O-17 yields from intermediate-mass stars published in the literature so far, we still get a too large solar abundance for this element, a problem already encountered in the past by other authors using different yield sets. Therefore, we conclude that in computing the O-17 yields from intermediate-mass stars some considerable sink of O-17 is probably neglected. The situation for N-15 is less clear than that for C-13 and O-17, mainly due to contradictory observational findings. However, a stellar factory restoring N-15 on quite long time-scales seems to be needed in order to reproduce the observed positive gradient of N-14/N-15 across the disc, and novae are, at present, the best candidates for this factory. Given the uncertainties still present in the computation of theoretical stellar yields, our results can be used to put constraints on stellar evolution and nucleosynthesis models.