An illumination device for generating light and supplying the light to an observation device used in endoscopy or microscopy comprises a light source having at least one LED and at least one optical waveguide to guide the light emitted by the light source. The proximal end of the optical waveguide is arranged on a side of the light source which faces the optical waveguide. The illumination device furthermore comprises a cooling device to dissipate heat generated by the light source, which cooling device has at least one first cooling element for dissipating the heat generated by the light source, which cooling element is arranged on a side of the light source which faces away from the proximal end of the optical waveguide. The cooling device has a second cooling element for dissipating the heat generated by the light source, which second cooling element is arranged on the side of the light source which faces the proximal end of the optical waveguide. The at least one optical waveguide passes through the second cooling element.