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The results of the study of the temperature dependence of attenuation and velocity of ultrasonic waves are presented for CaF2:Cr and CaF2:Ni crystals in which Cr2+ and Ni2+ ions substitute calcium ions, forming Jahn–Teller (JT) complexes [CrF8]6– and [NiF8]6–. The Cr2+ and Ni2+ ions in the fluorite structure have threefold orbital degeneracy in the ground state, are described by the T $$ \otimes $$ (e + t2) Jahn–Teller effect (JTE) problem, and have an adiabatic potential energy surface (APES) defined in the five-dimensional space of trigonal and tetragonal symmetrized coordinates whose lower sheet is a simply connected surface with orthorhombic minima separated by potential energy barriers. The temperature dependence of the ultrasonic attenuation and velocity exhibits anomalies typical of the relaxation contributions of systems of JT complexes in the low-temperature region. The effect of tunneling relaxation mechanisms (direct and two-phonon transitions) on the JT contribution to the complex elastic moduli and to the error in determining the relaxation time is analyzed. Based on the approach that takes into account both tunneling and activation mechanisms of relaxation, the activation energies and the constants characterizing these relaxation mechanisms are determined in CaF2:Cr2+ and CaF2:Ni2+ crystals.