High-resolution spectra of six core helium-burning `clump' stars and three giants in the open cluster M 67 have been obtained with the SOFIN spectrograph on the Nordic Optical Telescope to investigate abundances of up to 25 chemical elements. Abundances of carbon were studied using the C_2_ Swan (0,1) band head at 5635.5{AA}. The wavelength interval 7980-8130{AA} with strong CN features was analysed in order to determine nitrogen abundances and ^12^C/^13^C isotope ratios. The oxygen abundances were determined from the [O I] line at 6300{AA}. The overall metallicity of the cluster stars was found to be close to solar ([Fe/H]=-0.03+/-0.03). Compared with the Sun and other dwarf stars of the Galactic disk, as well as with dwarf stars of M 67 itself, abundances in the investigated stars suggest that carbon is depleted by about 0.2dex, nitrogen is enhanced by about 0.2dex and oxygen is unaltered. Among other mixing-sensitive chemical elements an overabundance of sodium may be suspected. The mean C/N and ^12^C/^13^C ratios are lowered to the values of 1.7+/-0.2 and 24+/-4 in the giants and to the values of 1.4+/-0.2 and 16+/-4 in the clump stars. These results suggest that extra mixing of CN-cycled material to the stellar surface takes place after the He-core flash. Abundances of heavy chemical elements in all nine stars were found to be almost identical and close to solar.