We study the rheological propertiesof the melts and the processes of structure formation in mixtures consisting of a copolymer of ethylene with vynil acetate (CEVA) and a copolyamide (CPA). It is estabilished that dipole-dipole interaction is realized between the CEVA and CPA macromolecules at the interface of the phases. We show for the first time that the CEVA microfilaments that form during flow of the CEVA/CPA blend melt have an unusual structure, the appearance of which is explained by the forced deformation of the CEVA in the mixture as the result of specific interaction of the macromolecules of the components at the interface of the phases. The longitudinal deformation capability of the CEVA/CPA blend melts may serve as a criterion of the degree of realization of the specific fiber formation (fibrillation) phenomenon. On the basis of study of the processes of breakdown of the CEVA microfibers in the CPA matrix, it is shown for the first time that they do not break down into drops in accordance with the Rayleigh-Weber-Tomotika wave mechanism, even at temperatures significally exceeding their melting point.