The fight against money laundering and terrorist financing has been on the rise in recent years, and continuous work is being done to improve the implementation and application of EU rules in order to suppress criminal activity as much as possible. In addition to EU regulations and rule books and decisions, Croatian Parliament passed the Law on the Prevention of Money Laundering and Terrorist Financing. The law prescribes measures, actions and procedures that need to be undertaken to prevent the money money laundering and terrorist financing. In the first part of this paper, the aim is to show all responsibilities of one bank as Law enforcement institution and what is necessary to ensure that the process of preventing money laundering and terrorist financing can be implemented. Banks are mandatory to assess and manage money laundering risk and terrorist financing, through risk factors they are mandatory to assess all clients, products, services and transactions that clients will deal with, delivery channels, and countries or geographical areas from which clients come from or do business in. After conducting a risk assesment, banks are required to enforce measures during establishing a business cooperation and during conducting occasional transactions. The enforcement of measures is carried out through client in-depth analyzes during establishing cooperation and through measures of constant monitoring during business cooperation. In the second part of the paper, the aim is to show an example of one bank, its meausers of constant monitoring, how these measures are beeing carried out and how the system is developed according to certain parameters, in order to make it easier for bank employees to enforce continuous monitoring measures.