To obtain an NOx absorbent material having better NOx absorbing performance and a catalyst for the purification of exhaust gas excellent in durability as well as in purifying performance.

The NOx absorbent material contains barium and an alkali metal and/or an alkaline earth metal other than barium. In the X-ray diffraction pattern of the NOx absorbent material a peak due to the (111) face of BaCO3 is present and the intensity ratio (IA/IF) of the intensity IA of the peak after long-term use to the initial intensity IF is 0.2-1. The catalyst for the purification of exhaust gas contains the NOx absorbent material and platinum and/or palladium. The above constituent metals of the NOx absorbent material are carried by an impregnation method using an aqueous solution of salts of the metals.