The peak of ultrasonic absorption observed at ≈13 K in ZnSe:Ni crystals with dopant concentration of 5.5 × 1019 cm–3 was interpreted as due to the Jahn–Teller effect. The dynamic contribution to the effective elastic modulus was accounted for and the temperature dependences of relaxation time, relaxed and unrelaxed modulus C44 were obtained. The procedure of accounting for the dynamic contribution resulted in a more accurate determination of the temperature of phase transition. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)