The importance of the paper is provided by the fact that multilingualism being one of the most important characteristics of the contemporary society envisages the study of two and more foreign languages at non-language higher education institutions. The present research aims to examine and reveal grammatical difficulties the students face while learning English as the first foreign language and Spanish and German as the second ones. The difficulties learners experience are mostly connected with interlanguage interference, in particular, Russian students' grammar interference. The methods used to achieve the goal focus on the analytical review of the contemporary research of the issue under study, the survey of the participants of the teaching experiment, and the method of mathematical statistics. The paper presents the findings of the experiment held by the Department of Foreign Languages at Law Institute of RUDN University (Peoples' Friendship University of Russia). The findings of the research can be used in teaching foreign languages for specific purposes in higher education institutions and as a ground for further development of the issue.