The kinetic modeling of carbon suboxide (C3O2) thermal decomposition and formation, transformation, and thermal decomposition of solid fullerene-like and soot-like carbon particles is carried out by one-step heating for the mixture of 0.33% C3O2 inAr within the temperature range of 1200 to 2250 K at the pressure of 5 MPa and for a two-step heating for the mixtures of 1%, 2%, and 4% C3O2 inAr within the temperature range of 2400 to 3750 K at 2 MPa. The formation of small carbon clusters up to C-30 in the gas phase and the formation, growth, transformation, coagulation, and thermal decomposition of the precursors, fullerene-like and solid-like solid carbon particles, are modeled with the help of a detailed gas-phase kinetic scheme combined with the kinetic scheme for heterogeneous reactions in the context of the discrete Galerkin method. The experimentally measured and calculated values of the induction period tau of solid carbon particle formation, the total yield of solid carbon particles Y, and the observable growth rate constant of solid carbon particles k(f) are compared and demonstrate a good agreement. The possible pathways of transformation of the precursors, fullerene-like and soot-like solid carbon particles, are analyzed.