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In the US, it was the formation of a new country. The first form of government after the revolution was the Articles of Confederation, which was a fairly weak central government, with the states having more power.
There were many problems with this government, not the least was it wasn't able to pay it's bills. Former soldiers were not getting the pay they were owed, and were on the verge of revolt. Other countries which were owed money were getting upset, and the central government was broke.
This state of affairs is what led to the Constitutional Convention in 1787, that eventually produced the Constitution.