A kinetic model of the heavy oil feedstock hydroconversion performed in continuous flow reactor in the presence of in-situ synthesized dispersed nanosize catalyst Molybdenum disulfide (MoS2) has been proposed. The kinetic parameters of heavy oil feedstock with different properties have been determined for the two process versions: with coke formation and without appreciable coke formation. It has been stated that hydroconversion in the presence of in-situ synthesized dispersed MoS2 (C(Mo) = 0.05% wt. (per feed)) corresponds to a first-order reaction for all studied feedstock samples. The rate and activation energy constants have been determined. It has been shown that the conditions of polycondensation products (coke) formation result in increasing process rate and decreasing activation energy.