Contemporary university education is based on the development of students' competences that is generally being understood as the unity of knowledge, skills and value attitudes. While knowledge and skills can be easily measured and evaluated in the teaching / learning process, value attitudes seem to fall in the category of more intangible things, the development of which could not be very easily tested and assessed. Therefore, value attitudes may not always be in the focus of attention of university teachers, although they seem to be responsible for nurturing value attitudes of students. The development of value attitudes in the process of plurilingual education is especially necessary as values can be the core or foundation that helps learners realize the necessity of learning languages, foster their motivation and expand their understanding and acceptance of diversity issues. Thus, the aim of this research was to find out the university teachers' views on the development of students' value attitudes in plurilingual education. The aim was specified by several research questions: why values should be integrated in the teaching of their subjects, what values could be developed within the framework of teaching their subjects at universities, and what teaching / learning methods should be applied. The research was qualitative, there were 10 teachers from different universities of Lithuania interviewed and it was carried out in 2017. The results of the current research were compared with the research into university teachers' viewpoints on the development of value attitudes conducted in 2013, when university teachers from Ukraine, Georgia, and Latvia were interviewed. The conclusion is made that university teachers are aware of the necessity of the development of values in plurilingual education, although they seem to lack the Know-How. University teachers have to create favourable learning environment, choose appropriate teaching / learning materials and apply suitable teaching / learning methods.