Possession has been scarcely studied in the variety of Spanish in contact with Mapudungun and in Chilean Spanish. In this contribution, we analyze the nominal possessive constructions found in a corpus of interviews with speakers from five communities: three Mapudungun-Spanish bilingual communities from the Araucania Region, one Spanish monolingual rural community from the Bio Bio Region, and one Spanish monolingual urban community from the Araucania Region. The possessive constructions found in the contact Spanish, rural Spanish, and urban Spanish varieties are analyzed and compared to describe the domain of possession and to propose some possible explanations from the perspective of language contact theory for the case of the Spanish spoken by bilinguals. From the corpus of transcribed interviews, nominal possessive constructions were selected, classified, described, and compared. Double possession with restrictive relative clauses, and unstressed possessive pronouns plus a prepositional phrase with genitive/specific value, showed a limited frequency of occurrence. These constructions are analyzed using the Code-Copying framework. This perspective accounts for the observed equivalencies between both languages in contact and the constructions emerging in the bilinguals' speech. This work contributes to the documentation of the variety and, more generally, to the description of the expression of possession in the Latin American contact varieties of Spanish.