In the present article the author gives evidence of effective application of cloud storage and on-line applications in the educational process of the higher education institution, as well as considers the problems and prospects of using cloud technologies in the educational process, when creating a unified educational space in the foreign language lessons at the linguistic university. Today there is a growing importance of cloud technology, which offers universities new opportunities to provide modern network technology-based applications, providing a high level of educational service. The pilot testing confirmed the didactic benefits of the cloud technologies: an intensive upgrading of learning content, the development of individual creative initiative, and self-organizational practice in the new educational environment. The novelty of this work is that the author suggests the use of cloud technologies in teaching foreign language (FL) at the higher educational institution in terms of using cloud platforms such as Google Apps Education Edition and Microsoft Live@edu, as well as Microsoft's cloud storage SkyDrive and AppleiCloud. The author suggests prospective lines for implementation of noted resources into the cloud technology-based educational process in both in-class learning and student self-study.