The article deals with the problem of forming morphological competence as an important component of the linguistic competence of intending Ukrainian language and literature teachers. Its structural components are determined: learning the system of morphological knowledge; mastering the skills and abilities to identify, to distinguish, to analyze morphological phenomena; conscious using them in speaking activities in different communicative situations. It is noticed that in the process of studying morphology, students should learn the regularities of functioning the language grammatical system, the issues of its researching at the present stage of Ukrainian linguistics development. Comparison of academic and school grammar contents give grounds for distinguishing a number of problematic issues that today have a little different coverage in theoretical linguistics and in the textbooks for higher education and secondary education institutions. It is stressed that future teachers should master the system of the newest morphological knowledge, in particular modern functional morphology, necessary for further successful professional activity. It is outlined the key issues of the section “Morphology”, the mastering of which will become the basis for students to understand the linguistic nature of semantic and grammatical word classes, understanding pronouns and auxiliary words peculiarities, the features of exclamations and onomatopoeias. It is noted that in the studying the main theoretical questions of morphology priority importance is given to the problem method. The examples of problematic tasks aimed at in-depth independent individual studying educational tasks by students, searching the information to prove or refute statement are given in the article. Some tasks and exercises are proposed, the content of which is determined by key skills and which are aimed at developing the basic students’ components of morphological competence. It was emphasized that in the process of doing such tasks cognitive, creative, activity, communicative skills of intending teachers are developed, which is an important part of their professional activity.