The right of the Member States to legislate on their own.
Basically, the EU only has the power to legislate when it is clearly conferred upon it. Topics not mentioned as common tasks in the European treaties therefore automatically remain under the power (competence) of the Member States.
However, the EU Court has been able to employ novel interpretation to increase EU integration by legalising EU decisions in areas that were Member States competence prior to the Court's new interpretation.
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See Categories of competence, Human rights and Discrimination.