In the article, the tendency to the formation of two strategies for higher education development in view of its quality was justified based on the authors’ fundamental research, new empirical data, modern world experience. The first strategy is to ensure the minimum sufficient quality of higher education, the second – to achieve the maximum perfect quality. Both strategies naturally anticipate and organically complement each other and are a powerful source of development in its synergy (dichotomous unity and struggle of opposites). Strategy-1 is based on mass standardized practice and accreditation mechanisms for ensuring threshold quality, strategy-2 is based on breakthrough innovations and ranking mechanisms for monitoring and motivating continuous quality improvement to its top levels. Progressive countries de facto make full use of both University development strategies. First, weak / backward higher education institutions (HEIs) are being tightened or cut off, in particular through the implementation of standards and recommendations, accreditation procedures within the framework of the Bologna Process. Second, in the intensifying competition, the best institutions are promoted to the level of the sub-world, world-class, including the extra class, using ranking mechanisms for assessing achievements as well as special initiatives of significant concentration and strong support of leading institutions in national policies and practices. The experience of the establishment and operation of the Ukrainian National Agency for Quality Assurance in Higher Education shows that so far, it focused de jure and de facto only on the first strategy, which is insufficient.
 At the same time, Ukraine lacks the implementation of strategy-2, primarily due to the lack of appropriate legislation, in particular, legislation on the implementation of the national HEIs ranking on the methodological basis of the Shanghai ranking (objectivity, transparency, validity, reliability, etc.). Direct use of leading international University rankings (Shanghai, Times, QS) is impossible due to the lack of world-class Universities (in the top 500 group) and sub-world-class ones (group 501-1000) according to the Shanghai ranking, the so-called candidates in world-class Universities, in Ukraine. According to the latest versions of the Times and QS rankings, Ukrainian HEIs positions have generally deteriorated. Regarding the Shanghai ranking 2021, Ukraine is not represented at all among 63 countries / territories in the general version as well as among 93 countries / territories in the sectoral version in 54 academic subject areas. As a result, the gap between Ukrainian Universities and the world's leading HEIs continues to widen. Recommendations for the immediate formation and implementation of strategy-2 for the higher education development in Ukraine are provided.