The purpose of the given study is to spot probable modus to teach English grammar to university students of non-linguistic specialities in order to find better ways to eliminate difficulties and succeed in training process. The research was conducted in the framework of making a choice between implicit and explicit methods of teaching English grammar to the students of medical and agrarian-technological institutes of Peoples' Friendship University of Russia ( Russian Federation). Using various ways of teaching English grammar the authors conducted some experimental inquiries. The researchers took into consideration that the aim of a grammar lesson is better achieved if practicing of English is combined with the identification and analysis of the structures the students have just used or are about to use in communication. It was clarified that basing on the principle that grammar acquisition includes two aspects: understanding of grammar structures and understanding of the situations where these structures are applied, a teacher could give his students exercises on these topics separately and then proceed to practicing texts and dialogues to confirm the acquired grammar knowledge. Reviewing the background of the issue, considering pros and cons, analyzing the peculiarities of the target audience (students of RUDN agrarian-technological and medical institutes) the authors came to some conclusions, which helped them to substantiate the chosen approach and share their experience in practicing it. The obtained findings show that what is required is a combination of both approaches with the prevalence of the implicit one.