The identity concept is analized and although the logical-essential (A=A) identity concept is criticised, we concentrate especially in the psycological and sociological concept to determine that the identity is a construction in which the identitary group is established from an opposition. Identity is a social and psycological phenomenon comparable to magic, which it doesn't mean that it doesn't exit, as in fact it works when two features occur: a.- to be accepted by the individual, and b.- to be socially supported. By applying the term "identity" in the immigration discourse, it is supported that the migrant identity is formed due to the exclusion, the rejection, the lack of integration or the marginalization of the receiving society. The construction of the migrants identity as such, or as members of national, cultural or religious identities, takes place from the immigration receiving societies. The legislation, the treatment received in the press, the integration measures, the discrimination, the term "sin papeles"(no identity papers, illegal),... are the ones which produce the identity as immigrants. To finish, the concept "cosmopolite" is tried to recover from the philosophycal exercise, as a review to the own customs, moving away from the relativist positions.