A catalytic reactor for generating a hydrogen-containing synthesis gas from a rich fuel/oxidizing agent mix. The reactor (1) includes a multiplicity of parallel passages which extend from an inlet side (6) to an outlet side (7). To achieve a compact overall form of the reactor (1), at least in a core region of a cross section through the reactor (1) all the passages are of a catalytically active nature. In a first longitudinal part (8) of the reactor (1), which includes the inlet side (6), the catalytically active first passages have a larger proportion of the surface area provided with a catalytically active coating than the catalytically active second passages in a second longitudinal part (9) of the reactor (1), which includes the outlet side (7) and adjoins the first longitudinal part (8).