Theoretical problems of neuropsychology of bilinguism are considered and dichotic experimental data on Spanish-Russian and Vietnameesse-Russian bilinguals are presented. Emphasis on the process of language acquisition permits to differentiate developmental stages of bilingualism and correspondent patterns of inter-hemispheric cooperation: tendency to right-hemispheric dominance at the very begining stages of second language acquisition, later much stronger than in vernacular left hemispheric dominance, and similar patterns of lateralization for both languages in balanced bilinguals.