The extraordinary activity of comet C/1995 O1 (Hale-Bopp) made it possible to observe the emission bands of the radicals C 2 and C 3 in the optical wavelengths range at heliocentric distances larger than 3 AU. Based on these observations, we perform an analysis of the formation of C 2 and C 3 in a comet coma at large heliocentric distances. We present the most complete chemical reaction network used until today, computing the formation of C 2 and C 3 from C 2 H 2 , C 2 H 6 , and C 3 H 4 as their parent molecules. The required photodissociation rates of C 3 H 2 and C 3 had to be derived based on the observations. The spatial distributions of C 2 and C 3 calculated with the chemical model show good agreement with the observations over the whole range of heliocentric distances covered in this work. Based on the production rates for C 2 H 2 , C 2 H 6 , and C 3 H 4 , abundance ratios are obtained for heliocentric distances r h ≥ 3 AU. In comet Hale-Bopp, C 2 H 2 and C 2 H 6 were measured directly by infrared observations only at heliocentric distance r h ≤ 3 AU . The model presented here greatly extends the heliocentric distance range over which hydrocarbons can be studied in the coma of comet Hale-Bopp. We discuss possible indications of these abundance ratios for the formation region of comet Hale-Bopp.