The article concentrates on the study of the contact of two cultures within the triad ‘real world — mental models — world of language’. Each of the worlds is viewed through the dichotomy ‘universal vs culture-specific’. The main emphasis is on the cognitive mechanisms underlying intercultural dialogue. We come to the conclusion that at the level of cognitive systems of two cultures the mechanisms of interactive alignment and inference are prevailing, at the level of mental spaces of the participants of the dialogue the mechanism of conceptual integration is at work. The contact of two cultures involves three mental spaces: 1) the mental space of one’s own culture; 2) the mental space of “other” culture; 3) integrated intercultural mental space. The latter inherits the roles and qualities of the two input mental spaces. The integrated mental space has its own emerging structure. Each of the three mental spaces is structured by its own frame. The third mental space is a result of the conceptual blending. This mental space is at the basis of intercultural discourse. The frame of this mental space structures and builds intercultural discourse. It helps to understand other culture, to infer conceptual information and find corresponding linguistic representations in each of the two cultures. All the above mentioned cognitive mechanisms providing the basis of two cultures contact involve knowledge of mental cultural models.