[eng] Results are reported for simultaneous experimental studies of the stress-induced magnetic induction and of anelasticity in a polycrystalline Ni–Fe–Ga ferromagnetic shape memory alloy. The authors found in the martensitic state a linear relationship between mechanically induced induction and stress amplitude, in contrast to a strong nonlinearity of the anelastic strain. This difference between elastic and magnetic responses to applied stress points to inefficient coupling between the motion of elastic twins/domain boundaries and magnetic domain walls. They argue that, in acoustic experiments, magnetic domain walls in Ni–Fe–Ga polycrystals perform only linear displacements within local potential minima, characteristic for the microeddy current magnetomechanical damping.