Exhaust purification device of an internal combustion engine

An exhaust purification device of an internal combustion engine wherein an NO.sub.x absorbent which absorbs NO.sub.x when an air-fuel ratio of an inflowing exhaust gas is lean and releases absorbed NO.sub.x when the oxygen concentration of the inflowing exhaust gas is lowered is arranged in an exhaust passage of the engine, and an amount of alkali metals, alkali-earth metals or rare-earth metals, contained in the NO.sub.x absorbent positioned on the downstream side, is made lower than an amount of alkali metals, alkali-earth metals or rare-earth metals, contained in the NO.sub.x absorbent positioned on the upstream side, to improve the reducing ability of the NO.sub.x absorbent positioned on the downstream side as compared to the reducing ability of the NO.sub.x absorbent positioned on the upstream side, NO.sub.x absorbed in the NO.sub.x absorbent being released from the NO.sub.x absorbent when the oxygen concentration of the exhaust gas flowing into the NO.sub.x absorbent is reduced.