Non-LTE analysis ( LTE is local thermodynamic equilibrium ) of the oxygen abundances for 51 Galactic A- , F- and G-type supergiants and bright giants is performed . In contrast with carbon and nitrogen , oxygen does not show any significant systematic anomalies in their abundances log \varepsilon ( O ) . There is no marked difference from the initial oxygen abundance within errors of the log \varepsilon ( O ) determination across the T _ { \text { eff } } interval from 4500 to 8500 K and the \log g interval from 1.2 to 2.9 dex . This result agrees well with theoretical predictions for stellar models with rotation . With our new data for oxygen and our earlier non-LTE determinations of the N and C abundances for stars from the same sample , we constructed the [ N/C ] vs [ N/O ] relation for 17 stars . This relation is known to be a sensitive indicator of stellar evolution . A pronounced correlation between [ N/C ] vs [ N/O ] is found ; the observed [ N/C ] increase from 0 to 1.6 dex is accompanied by the [ N/O ] increase from 0 to 0.9 dex . When comparing the observed [ N/C ] vs [ N/O ] relation with the theoretical one , we show that this relation reflects a strong dependence of the evolutionary changes in CNO abundances on the initial rotation velocities of stars . Given that the initial rotational velocities of these stars are expected to satisfy V _ { 0 } < 150 km/s , it is found that they are mostly the post first dredge-up ( post-FDU ) objects . It is important that just such initial velocities V _ { 0 } are typical for about 80 % of stars in question ( i.e . for stars with masses 4-19 M _ { \sun } ) . A constancy of the total C+N+O abundance during stellar evolution is confirmed . The mean value log \varepsilon ( C+N+O ) =8.97 \pm 0.08 found for AFG supergiants and bright giants seems to be very close to the initial value 8.92 ( the Sun ) or 8.94 ( the unevolved B-type MS stars ) .