Russian New University, one of well-established non-government universities in Russia, has started working on the Russian Ministry of Education and Science project aimed at the teaching of Russian language to every category of students worldwide via Internet. The working group for the project has conducted an in-depth study of the requirements for the educational levels and profiles of remote studying of Russian language abroad. Based on this study, RosNOU project team has decided to choose a cloud technology as the basis for realization of the project. By the proposed scheme, the same type of software is required for realization of the project, because it allows achieving the unity of standards for the preparation of educational content, as well as approaches for implementation of the educational process with the use of distant teaching technologies. The developed model and the concept of its managing mechanisms should be tested in order to make specific decisions about their implementation in practice of education.