Abstract: Apparatus for controlled low NO.sub.x combustion. First and second combustion zones are provided, each filled with a porous high temperature resistant matrix, the void spaces of which provide sites at which substantially all of the combustion occurs. The second zone is downstream of the first zone. Means are provided for mixing fuel and a gaseous source of oxygen and providing the resultant combustible mixture to the input end of the first combustion zone to establish fuel-lean conditions therein; and means for feeding the combustion products from the first zone to the second zone and augmenting same with further oxygen and sufficient additional fuel to create fuel-rich burning conditions therein to complete the oxidation of the products from the first zone.