Membership in the european union requires countries to have which type of government?

If one country wants to become an EU member state, they have to satisfy the “Copenhagen criteria”:
- a STABLE DEMOCRACY
And the rule of law
- a free-market economy
- the acceptance of all EU legislation, including of the euro.

To answer your question, a state has to have a representative democracy. EU countries do not have the same type of government because they have different histories. There are three types of government of the EU member states now:
Parliamentary republic (Italy, Germany, Greece — most of them actually)
Semi-presidential republic (Romania, France, Poland, Portugal)
Parliamentary constitutional monarchy (with a king/queen, like the UK, Belgium, Netherlands, Spain, Sweden, Denmark)

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