It has been shown that the nature of the support (MFI zeolite, aluminum-magnesium hydrotalcite, stabilized ceria, neodymia) has a significant effect on the stability of Ni and Ni-Co catalysts for partial oxidation of methane to synthesis gas and a less significant effect on the stability of the catalysts for dry reforming of methane to synthesis gas. It has been found that aluminum-magnesium hydrotalcite is the most advantageous support for nickel catalysts, because it reliably provides a high synthesis gas yield in partial oxidation and dry reforming of methane, whereas the MFI zeolite is a stable and selective support for Ni-Co catalysts for dry reforming of methane.