We derived atmospheric parameters and spectroscopic abundances for C and O for a large sample of stars located in the Hertzsprung gap in the Hertzsprung-Russell diagram in order to detect chemical peculiarities and get a comprehensive overview of the population of stars in this evolutionary state. We have observed and analyzed high-resolution spectra (R = 60,000) of 188 stars in the mass range 2-5 M_{sun}_ with the 2.7 m Harlan J. Smith Telescope at the McDonald Observatory including 28 stars previously identified as Am/Ap stars. We find that the C and O abundances of the majority of stars in the Hertzsprung gap are in accordance with abundances derived for local lower-mass dwarfs but detect expected peculiarities for the Am/Ap stars. The C and O abundances of stars with T_eff_< 6500 K are slightly lower than for the hotter objects but the C/O ratio is constant in the analyzed temperature domain. No indication of an alteration of the C and O abundances of the stars by mixing during the evolution across the Hertzsprung gap could be found before the homogenization of their atmospheres by the first dredge-up.