The influence of an external magnetic field on the complex elastic moduli of crystals with a sphalerite or zinc blende (ZnSe) and wurtzite (CdSe) structure lightly doped by Cr2+ ions has been investigated. Measurements have been performed in the frequency interval 26–32 MHz at 1.4 K. In II–VI crystals, bivalent chromium cations are triply orbital-degenerate in the ground state and, being in a tetrahedral environment, produce Jahn–Teller complexes. These complexes are described in terms of the T (Formula presented.) (e + t 2)-problem and exhibit the adiabatic potential energy surface with the global minima of tetragonal symmetry. It has been found that in ZnSe:Cr2+ crystals, a magnetic field directed along the [001] and [110] axes influences modulus (c 11 – c 12)/2 and does not influence modulus c 44. In CdSe:Cr2+ crystals, however, moduli c 55 and c 66, which are the analogs of (c 11 – c 12)/2 and c 44, depend on the magnetic field directed along the (Formula presented.) and (Formula presented.) axes, respectively. The discovered anomalous behavior of the elastic moduli with magnetic field has been treated in terms of a model that takes into account the crystal field, vibronic and spin-orbital interactions, and the contribution of the Jahn–Teller subsystem to isothermal moduli determined at a constant magnetic induction. Good agreement with experimental dependences of the elastic moduli in strong magnetic fields has been obtained, and it has been shown that the nonmonotonic variation in weak magnetic fields (below 2 T) should be associated with a magnetic field dependence of the relaxation time. © 2023, Pleiades Publishing, Inc.