'one country, two governments') presuppose that China is "one country" (or "one nation") in cross-strait relations, but they want to recognize the political situation in which the government of the People's Republic of China (PRC) and the government of the Republic of China (ROC) coexist.
This is mainly supported by some Kuomintang politicians who oppose the PRC's one country, two systems, and it was the U.S. government that first proposed it.
In 1990, under the support of the United States, the National Unification Council, chaired by President of the Republic of China Lee Teng-hui, proposed "One nation, two states" to the People's Republic of China, but the proposal was rejected because the People's Republic of China feared that the dialogue between the two central governments would be distorted.
When Chen Shui-bian, a member of the Democratic Progressive Party, was elected president of the Republic of China in 2000, then Kuomintang leader Lien Chan proposed "One nation, two states", "federal system", and "national unification system" again and opposed Taiwan independence.
This is a fact recognized by the world and a prerequisite for the peaceful resolution of the Taiwan question.