Global challenges are an objective factor influencing the development of socio-economic and socio-political subsystems of society. The influence of this factor is not uniform, causing a different impact on every social activity sphere. The actualization of challenge to people's health risk, determined by the widespread of the COVID-19 infection in 2020, has become the cause of changes in modes of operation for most of social institutes, including that of education. To implement the national governments' decisions concerning prevention of population's infecting with COVID-19, the administrations of most European universities have refrained from teaching educational programs in the face-to-face mode and adopted the decision of applying the distance form of training. This forced step by the universities has determined the raise in stakeholders' interest in the problematics of the quality of education obtained through the distance mode of higher education. In their attempt to provide the answer concerning the potential of the distance form of training in ensuring education quality, the authors of this article have conducted a poll of 544 students from higher education establishments of Eastern Ukraine. The answers obtained were analyzed by the following aspects: comparing education quality depending on the mode of obtaining it; perspectives of applying the distance form of education at each stage of higher education; efficiency of applying the distance training instruments in the training process. On the results of analyzing the respondents' answers, recommendations and conclusions as to the state of distance education and the perspectives of its development were formulated. Besides, the article offers a classification of distance education instruments and proposes recommendations concerning their application in the training process. The article's content will be of interest not only for specialists working at agencies that ensure quality of higher education, but also for stakeholders and administrations of the universities that are planning to raise the level of their presence at the education services market on account of implementing the distance training's potentials.