In 2018, Fortune’s Global 500 ranking included 111 firms headquartered in China—just a handful fewer than the United States’ 126. In 1995, only three Chinese firms made the list; in 2018, three were in the top 10. No wonder some observers predict that China will soon overtake the U.S. as the home to the highest number of Global 500 firms. It’s entirely possible that this could happen, but the triumph may be fleeting.In the late 1990s, Japanese firms came close to outnumbering U.S. companies on the list, until a combination of a graying workforce and declining productivity caused them to slide back off. Japan’s experience, which is similar to that of China today, provides an uncomfortable precedent for the consequences of a slowdown in domestic growth.To keep their places on the Global 500, Chinese companies will have to develop a global mindset more characteristic of multinationals from small countries like Switzerland, a transformation that has to date eluded most Japanese businesses.