The hydroconversion of heavy hydrocarbon feedstocks (fuel oil, tar, rubber, polymer waste, natural bitumen) in the presence of an in situ synthesized suspended nanosized molybdenum catalyst (NMC) is studied. The process is run with recycling of a portion of the unconverted residue containing the in situ synthesized NMC particles. To provide the required NMC concentration in the reaction zone, the process is conventionally divided into stages; at each one, a given NMC concentration is provided by the introduction of a certain amount of the catalyst precursor in the form of an aqueous solution of ammonium paramolybdate into the feedstock and the recycling of a portion of the unconverted residue formed at the previous stage which boils above 500 degrees C and contains the NMC. The balance amount of the unconverted residue boiling above 500 degrees C is used to regenerate the catalyst precursor.