Context. It is widely accepted that C 3 and in particular C 2 play an important role in the compositional classification of comets, and the most well-established classification scheme to date is indeed based on the Haser production rates of these two radicals. A link between both C 3 and C 2 and their actual parent molecules would therefore be desirable to allow both a physical and chemical interpretation of the compositional classification of comets. A first detailed study was performed by Helbert and collaborators for comet C/1995 O1 (Hale-Bopp), which suggested a link between these two radicals and the parent species C 2 H 2 , C 2 H 6 , and C 3 H 4 . Aims. We extend previous studies of the formation of C 3 and C 2 to other comets at smaller heliocentric distances. The proposed model for the formation of these two radicals is tested for these comets. Methods. We compare the observed radial column densities of C 3 and C 2 in the comae of the comets C/2001 Q4 (NEAT), C/2002 T7 (LINEAR), and 9P/Tempel 1 with the results of a one-dimensional multi-fluid coma chemistry model. The shape of the modelled radial column density profiles are compared with the observed profiles, and the production rates of the parent species are computed by fitting the observational data with the model. Results. We do not find that C 2 H 6 is a significant parent species of the observed cometary C 2 . Furthermore, electron impact reactions do not play an important role in the formation of C 3 . The model for the formation of C 3 and C 2 derived from comet Hale-Bopp is inconsistent with observations of these radicals in other comets.