Disclosed is an illumination system that simultaneously utilizes the blue, green, and red color mixing principle (RGB mixing) and the principle according to which a radiation emitted primarily by an LED is converted into light having a greater wavelength by means of a luminous substance, said luminous substance absorbing said radiation. At least two LEDs are used, a first LED emitting primarily in the range from 340 to 470 nm (dominant wavelength) and a second LED emitting in the red range between 600 and 700 nm (dominant wavelength). The green component is generated by the fact that the primary radiation of the first LED is converted at least in part by a green-emitting luminous substance that belongs to the class of oxinitridosilicates, comprises a cation M, and is of general formula M(1-c)Si2O2N2:Dc. M contains Sr as a component while D is doped with divalent europium, wherein M = Sr or M = Sr(1-x-y)BayCax with the stipulation x+y