The conditions for the generation and containment of relativistic electron beams in a tokamak discharge were studied by deliberately driving Ormak into a strong runaway regime. The experimental results show that beams with typical currents of 60 kA and mean electron energies of 3 MeV could be generated reproducibly and then contained safely overe‐folding decay times of 35 msec without damaging the machine. The experiments substantially confirm and extend the results of previous modeling studies on runaway discharges. They also implicitly define the experimental conditions for the establishment of a steady, toroidal beam‐plasma system that can be of interest for plasma physical studies.