Practical experience of teaching and training interpreters and translators in law setting shows that its efficiency depends not only on the starting level of the students' proficiency but also on the assignments used. Such parameters as the bulk of the material, the way it is put in and realized into learning are of primary importance. Another factor that can make effect on the development of professional skills and competencies of interpreters is the time limit. Interpreters-to-be must work in a definite period and consequently this ability should be trained while studying. The paper is focused on the modern lingo-didactic technologies used in training and teaching different kinds of linguistic mediation, namely translation and interpretation, to students of Law Institute, Peoples' Friendship University of Russia. The experience of teaching English and German as Languages for Specific Purposes is presented. The technologies such as different communicative dictations, mini projects, interactive summary and paraphrasing can help students to improve their interest to learning, increase motivation, and develop their teamwork and interaction abilities. Students' skills to self-learning are also developed.