TAIPEI, Taiwan — The party once ruled China, helping to vanquish Japan in World War II. Defeated by Mao Zedong’s Communists, it fled to Taiwan, where it imposed martial law for decades before grudgingly yielding to popular demands for democracy.

But now the days of power and wealth are gone for the Chinese Nationalist Party, or Kuomintang, as it struggles to stay relevant in Taiwan politics — a situation that has implications for Beijing and Washington.

After a disastrous performance in last year’s general election, the Kuomintang, also known as the K.M.T., lost control of the presidency for the second time since Taiwan’s presidential elections began in 1996. For the first time, it is a minority party in the island’s legislature.

“The K.M.T. is looking for its footing in a new environment,” said Nathan Batto, assistant research fellow at Academia Sinica and an expert on Taiwan’s elections. How it will adapt to challenges on several fronts is still an open question.