Carbon nanostructures were prepared by decomposition of polyethylene and polyvinyl alcohol using an iron catalyst at 600-750 degrees C under a nitrogen flow. Heating a uniform distribution of catalyst particles in the polymer bulk to 600 degrees C under flowing nitrogen led to the formation of amorphous carbon incorporating uniformly distributed catalyst particles. Subsequent heating of the samples to 750 degrees C in a nitrogen flow led to the catalytic graphitization of the amorphous carbon matrix with the formation of different carbon nanostructures, i.e. carbon nanotubes. The mechanism of the formation of the obtained carbon nanostructures is discussed.