An electrodeless discharge lamp apparatus is provided which is increased in heat dissipation, making it possible to adapt to an increase in output of the apparatus. The electrodeless discharge lamp apparatus comprises a bulb containing a discharge gas and a coupler accommodated in a cavity formed in the bulb for generating a high frequency electromagnetic field. The coupler has: an induction coil; a core inserted into the coil; a heat conductor for conducting heat generated from the coil and the core; and a bobbin made of resin which accommodates the core and the heat conductor therein, and which has the coil wound therearound. The bobbin is designed to be separated in a radial direction of the coil, so that it is possible to separately mold the respective parts of the bobbin. Thus, it is not necessary to form, in the bobbin, a draft angle which has been necessary in the prior art when molding a tubular-shaped bobbin, and it is possible to make the thickness of the bobbin thin and uniform, so that the proportion of the bobbin in the volume of the cavity can be reduced to increase the proportion of the heat conductor.