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The process of nucleation of multiwall carbon nanotubes in chemical vapor deposition process with nickel as catalyst and methane as a carbon precursor is analyzed. The nucleation is considered as a specific instability developed on the surface of a metal catalyst particle supersaturated with carbon. The energy released in graphitization of carbon from the metal-carbon solution is shown to be crucial for the nanotube nucleation. The energy released may be high enough for substantial metal heating resulting in partial liquefaction of the catalyst particle. The proposed mechanism can be called vapor-solid-liquid-solid (VSLS) as the catalyst particle may be in a mixed solid-liquid (or liquidlike) state during nucleation and unstable phases of nanotube growth.