This article reveals the role of educational and project activities in developing students’ research competencies in modern educational process at university. Students’ productive development is possible only with their comprehensive training for these types of activities. Insufficient theoretical, methodological, and practical development of this problem in Kazakhstani science determined the relevance of this article’s topic. The analysis of the study of theoretical sources and practical experience allows us to conclude that students are insufficiently prepared for educational and project activities in developing research competencies. Most students do not comprehend the importance of developing research competencies in educational and project activities, having a relatively general understanding of them. Therefore they practically lack the relevant skills and abilities. The direction of further research is developing a methodology for the development of students’ research competencies in project and research activities within pedagogical and musical disciplines in the university educational process.