Burner system for generating hot gas in a gas turbine plant, having a combustion chamber which comprises a combustion space (24, 26) oriented along a longitudinal axis, and having a burner head which has at least one oxidizer/fuel supply arrangement for supplying oxidizer and fuel into the combustion chamber as fresh gas components, comprising - one flow path in each case for fuel and oxidizer for supplying them into the combustion space (24, 26), wherein the flow paths upstream of a mixing space each having separate flow portions for separately guiding the fresh gas components, and the flow paths are combined in the mixing space, and - at least one first supply opening for supplying fuel into the mixing space, wherein the oxidizer/fuel supply arrangement comprises at least one further flow portion having a further supply opening, via which a portion of one of the fresh gas components for supplying into the combustion space (24, 26) can be supplied into a flow portion with the other fresh gas component, wherein the further flow portion is arranged and designed in such a way that, in the case of an unchanged geometry, the portion of the fresh gas component that flows via the further flow portion can be changed with the calorific value of the fuel, as a result of a changing pressure ratio, in such a way that the velocities at the first supply opening and/or at the further supply opening deviate from each other at most by a factor of 2, in particular at most by a factor of 1.5, preferably at most by a factor of 1.2, between a low-calorific design point and a high-calorific design point, wherein - the low-calorific design point corresponds to a design operating point with a low-calorific design fuel, the mass-specific calorific value of which is approximately 5 MJ/kg, and the high-calorific design point corresponds to a design operating point with a high-calorific design fuel, the mass-specific calorific value of which is barely 50 MJ/kg, - the thermal outputs of the two design points correspond to each other, and - the further supply opening is formed by at least one bypass opening, wherein the bypass opening is formed upstream of a fuel opening of a fuel channel in a wall of same, and wherein the further flow portion forms a flow connection between the flow paths of the oxidizer and the fuel. - one flow path in each case for fuel and oxidizer for supplying them into the combustion space (24, 26), wherein the flow paths upstream of a mixing space each having separate flow portions for separately guiding the fresh gas components, and the flow paths are combined in the mixing space, and - at least one first supply opening for supplying fuel into the mixing space, wherein the oxidizer/fuel supply arrangement comprises at least one further flow portion having a further supply opening, via which a portion of one of the fresh gas components for supplying into the combustion space (24, 26) can be supplied into a flow portion with the other fresh gas component, wherein the further flow portion is arranged and designed in such a way that, in the case of an unchanged geometry, the portion of the fresh gas component that flows via the further flow portion can be changed with the calorific value of the fuel, as a result of a changing pressure ratio, in such a way that the velocities at the first supply opening and/or at the further supply opening deviate from each other at most by a factor of 2, in particular at most by a factor of 1.5, preferably at most by a factor of 1.2, between a low-calorific design point and a high-calorific design point, wherein - the low-calorific design point corresponds to a design operating point with a low-calorific design fuel, the mass-specific calorific value of which is approximately 5 MJ/kg, and the high-calorific design point corresponds to a design operating point with a high-calorific design fuel, the mass-specific calorific value of which is barely 50 MJ/kg, - the thermal outputs of the two design points correspond to each other, and - the further supply opening is formed by at least one bypass opening, wherein the bypass opening is formed upstream of a fuel opening of a fuel channel in a wall of same, and wherein the further flow portion forms a flow connection between the flow paths of the oxidizer and the fuel.