Mastering academic writing skills in English is essential for future researchers. At present, AI language processing tools provide high-quality, accessible, and fast assistance for translation, editing, and stylistic enhancement of scientific texts. However, their use within English for Academic Purposes (EAP) courses generates mixed reactions among educators and raises ethical concerns. Our study aimed to explore the predominant perceptions of AI language processing tools by PhD students of the National Academy of Sciences of Ukraine (NASU) from the viewpoint of their integration into the academic English course taught in the first year of their PhD studies. The study involved 52 PhD students from various NASU institutes. They completed a survey with both closed-ended and open-ended questions regarding their previous and expected use of online translators, writing enhancement tools, and ChatGPT for research writing purposes. The results of the survey show that NASU PhD students have extensive experience with online translators, but are less familiar with writing enhancement tools and less certain about their potential use in the future. Almost a third of the respondents expressed reservations about using ChatGPT for academic writing due to academic integrity concerns. Most of the respondents (66%) agree that the basics of ethical use of AI writing and editing tools should be incorporated into EAP courses. One subgroup of the participants (n = 11) took part in a small-scale additional intervention focused on writing enhancement tools. They were asked to apply Grammarly, QuillBot, and ChatGPT to edit their course projects (presentations of the current state of their dissertation research) and compare these tools according to various criteria. The feedback provided by this subgroup indicates that they were most satisfied with the quality of editing provided by ChatGPT but found Grammarly and QuillBot easier to use and more suitable for superficial grammar checks. We found out that the AI tools helped participants achieve improvements primarily in such aspects as the use of articles, punctuation, use of prepositions, and elimination of redundancy. The study has significant pedagogical implications, promoting the wider use of AI tools in the context of teaching English for Academic Purposes and addressing appropriate teaching techniques and methods.