A model of free exciton magnetic polarons (EMPs) in diluted magnetic semiconductors is proposed on the basis of the localization of the hole in the magnetic potential well created by its own exchange field. The corresponding calculations of the free EMP binding energies, as a function ofMn2+ion concentration and temperature, are performed. The results are in good agreement with recent experimental measurements. It is found that free EMPs are stable up to relatively high temperatures(T≲30K) over a wide range of Mn concentrationsxwithout any other primary localization, e.g., alloy potential fluctuations. The dependence of the critical temperature of free EMP formation on the Mn concentration is determined for various diluted magnetic semiconductor materials, and is in good agreement with the experimental results forCd1−xMnxTe. The suppression of free EMPs under the application of an external magnetic field is also considered. ©1997 American Institute of Physics.