Hole-burning spectra of Eu3+ transitions in axial centers of alkaline-earth fluorides are presented. These spectra, along with optically detected nuclear-magnetic-resonance results, are used to analyze the hyperfine interactions in the F07 ground state and in the D05 optically excited state. The axial nature of these centers simplifed the theoretical analysis from which we obtained the nuclear-quadrupole-interaction strength and the nuclear-magnetic moment quenching factor. An improved value of the ratio of the quadrupole moments of Eu153 and Eu151 of 2.5530.001 is also given. © 1992 The American Physical Society.