The invention relates to a process burner (F) and to a method for operating a reactor (R) with a process burner (F) having at least one first (G) and one second primary supply duct (B), and at least two secondary supply ducts (N1, N2) that end within the first primary supply duct (G), wherein a combustion gas (1, 3) and an oxidant (2, 4) can be supplied respectively separate from one another via both the primary (G, B) and the secondary supply ducts (N1, N2). This is characterized in that the process burner (F) has a gas-permeable flow resistance element (P) which is arranged on the reaction chamber-side end of the first primary supply duct (G) and extends over the flow cross section of the latter.