In a burner for premixing-type combustion of a liquid and/or gaseous fuel, which essentially comprises hollow conical part-bodies (1, 2) positioned one upon the other, the center lines of which extend mutually offset in the longitudinal direction, whereupon tangential inlet openings (1b, 2b) are formed on both sides of the burner, a fuel (5a) is admixed to the combustion air (13) flowing into the interior (3) of the burner in that area. This admixture is accomplished via a number of nozzles (9, 10), which act in the region of the inlet openings (1b, 2b). The fuel through these nozzles is injected with a small spray cone angle in the longitudinal direction of the slot. The fuel vaporization takes place essentially only in the inlet openings of the burner, with the result that only a fuel vapor enters the interior (3). A further central nozzle (4) supplied with a liquid and/or gaseous fuel provides assistance in the form of a limit fuel quantity. The ignition of the mixture (4a, 5a, 13) takes place at the outlet of the burner, stabilization of the flame front (14) being brought about in the region of the burner aperture by a return flow zone (15).