The stability of the zeolite component and a La-Zr-HZSM-5/Al2O3 catalyst synthesized on its basis in the synthesis of lower olefins from dimethyl ether (DME) has been studied. It has been shown that both the zeolite component and the catalyst based on it exhibit highly stable catalytic properties. A high-temperature treatment of the zeolite component and the finished La-Zr-HZSM-5/Al2O3 catalyst with air and steam, respectively, leads to a significant increase in the catalyst selectivity for olefins, particularly propylene, while the activity in the DME conversion slightly decreases as the steaming temperature increases from 500 to 750A degrees C.