Results of a study of the methanol steam reforming (MSR) catalytic process in conventional flow and membrane reactors in the presence of Ni-0.2-Cu-0.8 and Ru-0.5-Rh-0.5 catalysts supported on ZrO2 with a monoclinic, tetragonal, and cubic structure have been described. The cubic structure of zirconia has been stabilized with ceria. The samples have been characterized by X-ray diffraction analysis, transmission electron microscopy, and the BET method. It has been shown that the catalytic activity of the composites depends on the type of the metals and the structure of the support. It has been found that the Ru-Rh/Ce0.1Zr0.9O2-delta catalyst exhibits the highest activity, whereas Cu-Ni/Ce0.1Zr0.9O2-delta is the most selective. A comparative study of the MSR process in conventional and membrane reactors with Pd-Ru and modified Pd-Ag membranes has been conducted. The membrane process with a membrane based on a Pd-Ag alloy in the presence of the Ru-Rh/Ce0.1Zr0.9O2-delta catalyst provides a similar to 50% increase in the hydrogen yield.