An aircraft beacon device of a wind power installation, to be arranged on a gondola of the wind power installation, comprising at least three omnidirectional emission sections arranged concentrically in a ring around a common mid-axis, each omnidirectional emission section comprising a lens section arranged concentrically in a ring around the mid-axis, with a beam plane defined perpendicularly to the mid-axis, and at least one lighting ring having lighting means arranged concentrically in a ring around the mid-axis in order to emit light through the lens section, wherein each lighting ring is configured in order to emit light with a central emission direction which makes an emission angle with the beam plane, and wherein the emission direction depends on an axial position of the lighting ring with respect to the lens section, wherein at least one omnidirectional emission section comprises at least two lighting rings offset axially with respect to one another for emission with different emission angles.