In many cases they were forced to retreat, given guerrilla wars in their colonies. In other cases they sometimes granted independence just a rebellions started. The most ferocious colonial wars (post 1945) include the French against the Viet Minh in 1946-1954 and in Algeria (1958-1962). Portugal clung on till 1974. France and Portugal suffered very serious defeats.
I assume this question applies to the Allied European Powers which still had empires at the end of World War 2. Let us say that they were not motivated entirely by the need to do a good thing. In World War 2, the cooperation of the imperial possessions was necessary, lest they switch sides and supply manpower and material to the Axis. Their independence, at least in the nominal sense, after the war was the price of that cooperation. Since Imperialism was going out of fashion anyway, it was a reasonable trade, but the European powers which fared poorly in World War 2 (France, Belgium, the Netherlands) gave up their empires more stubbornly than did Great Britain.
why did many European settlers want to leave their homeland
What_were_the_seven_European_powers_that_eventually_divided_up_Africa
European powers,however the Arabs where resistant
the United States, Great Britain, and France
European monarchs were offended by the Monroe Doctrine because it asserted that the Western Hemisphere was closed to future colonization by European powers and any attempt to do so would be seen as a threat to the United States. This challenged their imperial ambitions and interests in the Americas, leading to resentment and opposition from the European powers.
qing
What_were_the_seven_European_powers_that_eventually_divided_up_Africa
france gave up colonies in southeast Asia?
argentina gave up powers because peron crackdown on basic fdreedoms and made people very unhapphy about it
European powers,however the Arabs where resistant
Prevent European powers from dividing up China.
League of Nations
the United States, Great Britain, and France
When Leo decided to leave the Elders he took a "fall from grace" off the Golden Gate Bridge, meaning he gave up his elder powers to be with his family.
The empires split up into smaller territories.
European monarchs were offended by the Monroe Doctrine because it asserted that the Western Hemisphere was closed to future colonization by European powers and any attempt to do so would be seen as a threat to the United States. This challenged their imperial ambitions and interests in the Americas, leading to resentment and opposition from the European powers.
The states gave up some of their power in order to form a Federal union.
qing