Context. Some O and B stars show unusually strong or weak lines of carbon and/or nitrogen. These objects are classified as OBN or OBC stars. It has recently been shown that nitrogen enrichment and carbon depletion are the most likely explanations for the existence of the ON class. Aims. We investigate OC stars (all being supergiants) to check that surface abundances are responsible for the observed anomalous line strengths. Methods. We perform a spectroscopic analysis of three OC supergiants using atmosphere models. A fourth star was previously studied by us. Our sample thus comprises all OC stars known to date in the Galaxy. We determine the stellar parameters and He, C, N, and O surface abundances. Results. We show that all stars have effective temperatures and surface gravities fully consistent with morphologically normal O supergiants. However, OC stars show little, if any, nitrogen enrichment and carbon surface abundances consistent with the initial composition. OC supergiants are thus barely chemically evolved, unlike morphologically normal O supergiants.