The article presents the current tendencies in teaching English for Specific Purposes (ESP) for students of nonlinguistic specialities in the European context. The author analyses the requirements of English language proficiency set by the Common European Framework of Reference for Languages (CEFR), in the context of European integration processes. The National ESP Curriculum for Universities (2005) focuses on the necessity to acquire professional and functional communicative competence in English by the graduates, providing an opportunity for effective functioning in a professional environment. The current challenges in the ESP field in Ukraine are caused by the integration of the Ukrainian education system into the international academic community. The present situation of ESP teaching, learning and assessment does not satisfy the needs of students of non-linguistic specialities in Ukrainian higher educational institutions. The author discusses the idea of incorporating international English tests, such as FCE, CAE, IELTS and TOEFL in a higher education environment in Ukraine as a part of teaching ESP. The possibility of gaining the international experience in the field of certification and evaluation of studentsі English language proficiency level in accordance with the European requirements and criteria will help future specialists to develop their professional foreign language competence. The improvement and development of new forms and methods of ESP training and assessment in accordance with CEFR will give an opportunity for students to succeed in the competitive job market in the future.