The Rada of the Belarusian Democratic Republic has operated as a government in exile for more than a hundred years.

When a country is invaded, or there is a popular revolt, the government sometimes has to flee. That government in exile maintains its right to lead the country. But it operates from a foreign nation, waiting for a friendlier political climate – or a revolution – so that it can return. During the Iraqi invasion of Kuwait, for example, the Emir of Kuwait and his government operated a massive anti-Iraq propaganda campaign out of Saudi Arabia.
Most governments in exile last only a few years. They either return to rule or dissolve when it becomes apparent that a return is impossible. Some governments, though, are more persistent.
Following the collapse of the Russian Empire in the wake of World War I, territories across Eastern Europe began to look to new governance. In December 1917, delegates from across Belarus gathered together in Minsk to talk about what should happen. This First All-Belarusian Congress was broken up by Russian Bolsheviks, and Minsk soon fell under the control of Germany, but the council persisted. In 1918, it declared a new state: the Belarusian Democratic Republic.
This state did not last long. When the council declared its independence the area was still under German control. And when the Germans left, the Russians returned, and a competing Socialist Soviet Republic of Byelorussia was declared. The council (the Rada of the Belarusian Democratic Republic) fled to nearby Lithuania in 1919… and it has remained in exile ever since.
Belarus joined the Soviet Union. The Belarusian Democratic Republic maintained a government in exile and pressed for a return. They almost returned once, after the collapse of the Soviet Union, but would only hand over power to a democratically elected government. And Belarus’ only democratic election ended with Alexander Lukashenko taking power… which he has not given up since.
The Rada remains in exile today, mainly as an organisation to promote democracy in Belarus. It has been a “government” in exile for nearly a hundred and three years now, easily the oldest such entity still in operation today.
[Thanks to Today I Learned.]