A light source device in which the radiated light from the dielectric barrier discharge lamp can always be stabilized even if the discharge vessel of the dielectric barrier discharge lamp is large or the load on the tube wall within the discharge vessel is small. This is achieved according to the invention by the provision of a light source device having a discharge lamp which has a generally cylindrical, coaxial double-tube arrangement of an outer tube and an inner tube, in which there is an outer electrode on the outer tube, in which there is an inner electrode on the inner tube, and in which a discharge space between the inner and outer tubes is filled with a discharge gas for formation of excimer molecules by a dielectric barrier discharge, and of a power source for operating this discharge lamp in accordance with the relationship: Vs/Vp.ltoreq.0.5 where Vs is the starting voltage and Vp is the voltage applied to the discharge lamp during steady-state luminous operation.