The ROC government was founded in 1912, retreated to Taiwan in 1949, and continued to claim that it represented all of China until Lee Tang-huei became president in 1992 in Taiwan's first presidential elections (something which the US still does not have.)

Since both the PRC and ROC claim that Taiwan is Chinese territory, the ROC technically is not in exile because it is still on Chinese territory. The fact that the ROC was founded in 1912, twenty-two years before the founding of the PRC, makes many Chinese think that it is the more legitimate government because it is senior to the PRC.