A low NOx combustion process and burner apparatus in which a mixture of a primary fuel and air, with the air in excess of the stoichiometric requirement, is passed to a surface burner element. The mixture is distributed over the downstream side of the element where it is combusted in a primary combustion zone. Secondary fuel is mixed with surface combustion products from the primary zone and then combusted in a secondary combustion zone with a portion of excess oxygen from the surface combustion products. In certain embodiments the temperature of surface combustion products is reduced by heat transfer to the surface burner element, and in another embodiment by heat transfer to a screen or other element placed within the primary combustion zone, from which the heat is then extracted to a load, and in another embodiment by mixing the additional fuel or combustion products with cooled furnace gases. In other embodiments the placement of the secondary fuel jets is varied to achieve different combustion results.