Experimental techniques for irradiating primate and rat brains by a narrow 78Kr beam with an energy of 2.58 GeV/n extracted from the JINR Nuclotron is described. The brain is irradiated near the F3 focal point located in the experimental hall of Building 1 of the JINR Laboratory of High-Energy Physics (LHEP). The beam profile is measured with multiwire ionization chambers and radiochromic films, and its quality is monitored using time-of-flight scintillation counters. The radiation dose absorbed by the irradiated object is measured using a dosimetric ionization chamber with tilted electrodes. This air-filled chamber has been designed so as to suppress the effect of ion column recombination in the tracks of high-Z nuclei. The extracted beam of 78Kr ions is calibrated and monitored using nuclear photoemulsions and by comparing the readings from the standard ionization chamber at the beam extraction point with the ion counting rate in scintillation counters. The experiment benefits from Nuclotron’s stable operation and from the high intensity of the 78Kr beam reached in the 55th run (~2 × 106 ions per beam impulse at the F3 focal point). In this unique radiobiological experiment, the effects of the heavy ions of galactic cosmic rays on cerebral cognitive functions of astronauts are emulated and investigated.