Rapid globalization in all spheres of modern life enhancestherole of international communication focused on global ties formation, especially for the countries which find themselves in situations of conflict, including war, civil war and/or occupation. For such countries the role of English as lingua franca plays an imperative role and thus further intensifies the need in well-trained human resources with a good command of foreign languages. Despite the national understanding and governmental support in developing the foreign language proficiency of Ukrainian higher educational establishments’ graduates, the ESP teaching and learning is presently facing numerous challenges in Ukraine. The present article deals with the analysis of the up-to-date ESP teaching and learning difficulties at tertiary level on the basis of some twenty years of the ESP teaching experience. The study shows that ESP teaching management, including program and syllabus compilation processes currently need universally agreed standards as the number of contact hours allocated, the selection of courses and their combination as well as the choice of themes under study within the scope of the same major differ significantly from university to university. There is a constant need to provide for teacher-training programs; requirement to supply modern and relevant textbooks; necessity to enhance students’ motivation and improve their communicative competences. Some possible solutions to achieve the educational results, to successfully satisfy the learners’ specific needs and to overcome the existing hardships in teaching English to non-English majors are offered.