Electrodeless low-pressure discharge lamp having a discharge vessel which is sealed in a gastight manner and is filled with an ionisable metal vapor and a rare gas, which lamp has a cylindrical core of a magnetic material in which during lamp operation an electromagnetic field is generated in the discharge vessel by a metal wire winding surrounding the core and a high-frequency electric power supply unit connected thereto, the magnetic material core being provided with a cooling body consisting of a heat pipe which is located at the area of the longitudinal axis of the core and is surrounded by the core at least as far as the proximity of its first end, while the second end of the heat pipe is maintained at a relatively low temperature.