In the field of translation theory, owing to the new functional paradigm with its antropocentrism in the investigations, not only the approaches to the translation per se have changed, but also the scope of issues concerned with researches of this multidimensional and multifaceted phenomenon within the multicultural spaces through the prism of cognition has expanded. Subject. The cognitive aspects of translation and cognitive aspects of strategies in translation continue to give rise to new debates and, at this point, there is an inevitable necessity to apply the interdisciplinary approach within the framework of semiotics, pragmatics, semantics, sociolinguistics, etc. in the research of the central categories of translation theory, such as equivalence, in the light of modern cognitive paradigm. Since it is widely accepted that cognitive spaces are marked by cultural-specific differences, a comparative analysis of Spanish and Russian lexicological data can reveal and demonstrate two-dimensional national specificity of Spanish language which is manifested in non-equivalent and background lexical units and which imposes international and intervariant pragmatic restrictions on their choice and use in different types of communicative and pragmatic situations in accordance with communicative and pragmatic norms of the Spanish language and its variants. The objective of this article is to consider the functioning of non-equivalent lexical units in the cognitive space of translation, making a special reference to the Spanish-Russian language combination. Results. This article suggests strategies of conveying the precise meaning of these units at the moment of transferring and adequately restoring the sense as a fundamental condition of efficient communication. Methods of semantic and comparative analysis are used in this study. The practical value of the research is to use the results for fundamental studies within the field of translation theory and translation teaching.