Final answer:
Jiang Jieshi and Mao Zedong were fighting a civil war for control over China, with Jiang leading the Nationalists and Mao leading the Communists. After initially uniting against the Japanese invasion during WWII, their conflict resumed afterwards, ending in a Communist victory and the proclamation of the People's Republic of China by Mao in 1949.
Step-by-step explanation:
Jiang Jieshi (Chiang Kai-shek) and Mao Zedong were fighting in China because Nationalist leader Jiang was fighting a civil war against communists led by Mao. The origin of the conflict can be traced back to the different visions for China held by the Guomindang (GMD) or Nationalist Party, led by Jiang, and the Chinese Communist Party (CCP), led by Mao Zedong. Their struggle included a complex history of temporary alliances, such as the Second United Front during the Japanese invasion of China and sporadic civil conflict.
Following the defeat of Japan in World War II, the civil war resumed, ultimately leading to a Communist victory. By May 1949, Mao Zedong proclaimed the establishment of the People's Republic of China. Jiang and the Nationalists, despite support from the United States, were defeated and retreated to Taiwan, where they established a separate government that was recognized as the legitimate government of China by many Western nations until the 1970s.