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It is carried out the analysis of the share of cash outside the banks in the money supply in Ukraine within 2013-2017 and the integral indicator of the level of the shadow economy in Ukraine for 2010-2017. The dynamics of the main indicators of functioning of the payment cards market of Ukraine during 2012-2017 is analysed. The main tendencies of development the market of payment cards in Ukraine are considered. In particular, the dynamics of the number of holders of payment cards and their issuing banks, the development of electronic payment infrastructure, the types of payment cards issued by Ukrainian banks by types of carriers etc. formations, in terms of payment systems, dynamics of the structure of operations using payment cards by volume and quantity are considered in this research. On the basis of the results of the analysis, we have concluded that there is a development of cashless payments by payment cards in Ukraine. The strategic direction for the development of cashless settlements in transport infrastructure has been revealed due to the use of payment contactless cards as an innovative means of payment for services of transport organizations.