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The intersection problem for Z2Z4-additive (extended and nonextended) perfect codes, i.e., which are the possibilities for the number of codewords in the intersection of two Z2Z4-additive codes C1 and C2 of the same length, is investigated. Lower and upper bounds for the intersection number are computed and, for any value between these bounds, codes which have this given intersection value are constructed. For all these Z2Z4-additive codes C1 and C2, the abelian group structure of the intersection codes C1 cap C2 is characterized. The parameters of this Abelian group structure corresponding to the intersection codes are computed and lower and upper bounds for these parameters are established. Finally, for all possible parameters between these bounds, constructions of codes with these parameters for their intersections are given.