As practice shows, one of the main modern challenges for national central banks in the field of payment and settlement systems is the development of innovations and improvement of national payment systems in conditions of globalization. Taking into account the foregoing, the scope of this study is to solve the scientific problem of developing of directions for modernizing the national payment systems in accordance with modern trends in the development of financial markets, implemented on the basis of expanding institutional and infrastructural interaction both at the national and international levels, considering the strictest criteria of reliability and efficiency. To achieve this goal, in the article were solved tasks of analyzing the evolution of payment systems in the Republic of Moldova, as well as payment systems of a number of countries from the European Union, the possibility and feasibility of introducing in national legislation of certain provisions of Payment services Directive 2015/2366 (PSD 2), implementing in the Republic of Moldova of a modern Instant Payments System, accession of the Republic of Moldova to the Single Euro Payments Area (SEPA), and were proposed recommendations on some directions of development of the system of payment and settlement services in the Republic of Moldova.