For a stay of more than 3 months, family members of an EU citizen, but who are not themselves EU citizens, must:
be in possession of a valid passport and a visa if necessary;
make a declaration of arrival in their new commune of residence;
apply for a residence permit for a family member of an EU citizen.
The documents required for a residence permit are as follows:
a complete copy of the travel document (passport);
a certificate proving the bond of marriage, a registered partnership, family ties or the lasting relationship;
a copy of the registration certificate of the EU citizen they are joining, or a residence certificate if they are joining a Luxembourg citizen;
a photograph compliant with OACI/ICAO standards (recent photograph, in colour, good quality, full face, format 45 / 35 mm);
for dependent direct relatives in the ascending or descending line: any document proving that the head of the family is responsible for the applicant (for example: tax return, invoices relating to the child's schooling if he/she is over 21 years of age, invoices relating to keeping the person in the family home, etc.).
For more information, check with the authorities responsible for issuing residence cards: Immigration authorities of the Ministry of Foreign and European Affairs (Direction de l’i mmigration du Ministère des Affaires étrangères et européennes).