The problem of becoming and development of the Eurobonds market of Ukrainian banks which are to one of perspective directions of bringing in of foreign capital in a bank sector have been considered. The features of emission of the eurobonds of banks have been elucidated. The analysis of modern state of bank eurobonds have been carry out and the most attractive offers for investment have been determined. Key problems that impede the development of domestic banks on the international debts liabilities market have been revealed. Subsequence prospects of the functioning of the banks euroborrowings have been outlined.