Decomposition of high-purity methane in the presence of alpha -Fe-based catalysts to produce filamentous carbon was investigated. The reaction was studied in the temperature range of 650 to 800 degreesC. Filamentous carbon was demonstrated to form at temperatures not lower than 680 degreesC in the presence of both bare alpha -Fe and catalysts based thereon with admixtures of various hard-to-reduce oxides (SiO2, Al2O3, ZrO2, and TiO2). The maximal carbon yield, 45 g per g of iron, was obtained with the Fe/SiO2 catalyst comprising silica in amounts of 15 wt%. XRD and high-resolution electron microscopy were used for studying the carbon deposits. The data obtained allowed the conclusion on the essential influence of the chemical nature of the hard-to-reduce oxide admixture in the iron catalyst on the microstructure and morphology of the carbon filaments. Depending on the admixture, specific shapes of filaments and nanotubes predominated. Carbon nanotubes with thin walls built up by coaxial cylindrical graphene layers were formed in large amount over the Fe/Al2O3 catalyst. Centers of growth of octopus-like nanotubes were observed.