Abstract: In a premixing burner of the double-cone design for operating an internal combustion engine, a combustion chamber of a gas-turbine group, or a firing plant, having a high-pressure atomization nozzle (3), arranged at the cone apex, for atomizing liquid fuel, which high-pressure atomization nozzle (3) consists of a nozzle body in which at least one feed passage (24) is arranged for the liquid fuel (12) to be atomized, which can be fed at a pressure greater than 100 bar, and this feed passage (24), with or without a turbulence chamber (25) arranged in between, is connected via at least two nozzle bores (18) to the interior space (14) of the burner, the nozzle bores (18) are aligned with the zones of high air velocity in the burner, and the angle (.beta.) between the fuel-droplet spray (4) and the longitudinal axis (5) of the burner is at least as large as the cone half angle (.beta.) between the sectional cone bodies (1, 2) and the longitudinal axis (5) of the burner.