Hydrodesulfurization (HDS) of dibenzothiophene (DBT), hydrogenation (HYD) of biphenyl (BP) and 3,3＇-dimethylbiphenyl (3,3＇-DMBP) and their competitive reactions were carried out over a novel Co-Mo/carbon catalyst. Studies were made with a batch stirred micro-autoclave reactor, 100 ml, at temperatures of 300-320 degrees C and 2.9 MPa H-2. The HDS reactions were found to proceed via a network of sequential and parallel reactions and a computer model was developed which could be used to determine all the individual rate constants in the reaction scheme by matching experimental product composition data to theoretical curves as a function of conversion and/or reaction time. Unfortunately, with limited data, many different sets of rate constants can provide good matches with the experimental data. In order to obtain a unique solution for the set of rate constants two boundaries were found necessary. One is the relative hydrogenation activity of DBT to that of biphenyl which can be established with separate competitive experiments. The other is to consider the thermodynamic limitations, on the reactions of refractory sulfur compounds which proceed via ring hydrogenation. The rates of hydrogenation of BP and 3,3＇-DMBP were found to be much lower than the rates of HDS of DBT. In addition, it was established that there was almost no inhibition on the HDS of DBT by BP and/or 3,3＇-DMBP.