Single crystals BaMgF4 (BMF:Ce3+) doped with Ce3+ and codoped with Ce3+ and Na+ were grown by the Czochralski technique. The optical and electron spin-resonance (ESR) spectra of Ce3+ in the BMF:Ce3+ crystals have been measured at room and low temperatures, respectively. The experimental results show that there are, at least, two distinct Ce3+-substitutional sites in the BMF:Ce3+ crystals. In order to identify the Ce3+-substitutional sites, we have taken X-ray oscillation photographs. The additional satellite reflections observed in the photographs suggest that the BMF:Ce3+ crystals have a commensurate superstructure with twofold periodicity along the a-, b- and c-axes of the basic structure, respectively. The superstructure can explain the presence of two distinct Ce3+-substitutional sites in the BMF:Ce3+ crystals.