[en] In future, electricity could be produced in fusion power plants. One of the steps towards development of fusion power plants is the construction of an experimental fusion reactor ITER where deuterium (D) and tritium (T) will be fused and energy will be released. As natural concentrations of T are extremely low, the T as fusion fuel will have to be produced artificially. A series of calculations were made to investigate the possibility of producing small quantities of T for experimental fusion reactors such as JET and ITER in a small research reactor like the TRIGA Mark II reactor at the Jozef Stefan Institute (JSI). The T production is the largest if all irradiation channels in reactor's reflector are filled with LiAlO₂ samples. When samples are inserted, the excess reactivity decreases by around 200 pcm. In the second part of the work an estimate was made of how long the reactor can operate with current fuel supplies. Calculations were made with the TRIGLAV computer code. TRIGA can operate at full power for at least 2,860 days, during which 152 mg of T could be produced. We conclude that small TRIGA reactors can not produce any significant quantities of T for the needs of the future experimental fusion reactors. (orig.)