The present invention provides a method of removing harmful gases from an automobile exhaust. The method of the invention comprises contacting a thermally stable NO.sub.x trap composition with a first exhaust gas mixture at a temperature of at least 200.degree. C. The first exhaust gas mixture includes exhaust gases from an internal combustion engine operating in a fuel-lean condition. After, NO.sub.x has been absorbed onto the NO.sub.x absorber material, the NO.sub.x trap composition is then contacted with a second exhaust gas composition. In this step, the second exhaust gas mixture includes exhaust gases from an internal combustion engine operating in a fuel-rich condition. The present invention also provides the NO.sub.x trap composition used in the method. The NO.sub.x trap of the invention includes a precious metal, a NO.sub.x absorber material, an oxide that inhibits the decrease in NO.sub.x storing ability of the NO.sub.x trap composition, and a support material.