The energy resolution of different-geometry LaBr3:Ce and CeBr3 scintillation crystals grown by the Institute of Solid State Physics (Russian Academy of Sciences) by the order of the Skobel’tsyn Institute of Nuclear Physics (Moscow State University) was measured. The measurements were taken at energies of detected γ rays ranging from 20 keV to ∼5 MeV. The samples under investigation were shaped as cylinders with a diameter of 0.5 cm and heights of 1.5 and 3.0 cm. The positional resolution along the crystal axis was also investigated for the CeBr3 crystals by measuring the amplitudes of the scintillation signals from the opposite crystal ends. It was shown that the ratio of these amplitudes was dependent on the distance from a crystal end surface to the interaction point of a γ quantum inside the detector according to the linear law. The positional resolution along the crystal length appeared to be comparable to the crystal diameter. The results of the study suggest that CeBr3 crystals have a great potential as position-sensitive elements of space-sensitive detectors for high-energy charge particles and γ rays.