An electrodeless discharge lamp operating device including a light-transmitting discharge bulb 120, an induction coil including a core 103 and a coil 104, and a ballast circuit 140 for supplying a high-frequency power to the induction coil. The operating frequency of the ballast circuit 140 is in the range of 80 kHz to 500 kHz, and where the operating frequency of the ballast circuit 140 is f (kHz) and the power input to the discharge bulb 120 is P (W), the rare gas pressure p (Pa) in the discharge bulb 120 satisfies the relationship of the following expression:

##EQU1##

(where A, B and C are constants having the following values: A=4.010⁴, B=3.510⁴ and C=6.2), and the power input P to the discharge bulb 120 is 7 W at minimum and 22 W at maximum.