Abstract-The electronic and crystal structures of SrMgF4 single crystals grown by the Bridgman method have been investigated. The undoped SrMgF4 single crystals have been studied using low-temperature (T= 10 K) time-resolved fluorescence optical and vacuum ultraviolet spectroscopy under selective excitation by synchrotron radiation (3.7-36.0 eV). Based on the measured reflectivity spectra and calculated spectra of the optical constants, the following parameters of the electronic structure have been determined for the first time: the minimum energy of interband transitionsEg= 12.55 eV, the position of the first exciton peak En=1= 11.37 eV, the position of the maximum of the 'exciton' luminescence excitation band at 10.7 eV, and the position of the fundamental absorption edge at 10.3 eV. It has been found that photoluminescence excitation occurs predominantly in the region of the low-energy fundamental absorption edge of the crystal and that, at energies above Eg, the energy transfer from the matrix to luminescence centers is inefficient. The exciton migration is the main excitation channel of photoluminescence bands at 2.6-3.3 and 3.3-4.2 eV. The direct photoexcitation is characteristic of photoluminescence from defects at 1.8-2.6 and 4.2-5.5 eV.