From  the  process  of  globalization  of  law,  the  comparative constitutional law has gained a leading role for a better understanding and solving old and new constitutional national and international challenges. Therefore, some assumptions and considerations to take into account are presented for the development of the national constitutional order within the framework of the comparative constitutional law, such as universality and relativism of human rights; the concept of power and constitutional democracy; standards of free elections and judicial independence; freedom of expression, media pluralism and access to public information; the economic,social and cultural rights; the new fundamental rights.