In the last several years, the European societies, that in their majority were fairly uniform as far as race, culture or religion, have been converted into intercultural places where many different visions of the world live together. Together with a factor of exogenous plurality, produced by the increase in immigration, an internal desegregation should also be highlighted in our own societies. In this new environment of diversity, it is without a doubt, difficult for the Law to accommodate all the different ethical, religious or cultural demands of the people. In my paper I study the means of accommodation rooted in our legal tradition such as: the conscientious objection, the agreements of the State with religious groups, mediation and arbitration as a way of accommodation of plurality in the field of Family Law, etc. I conclude by stressing the fact that allowing space for diversity does not mean giving up our own values. Quite the opposite, accommodation comes from our own values: that is, from the respect for freedom and non-discrimination, founded on the dignity of the person.