As financial institutes provide their customers new technology channels it is argued that self-service technologies offer benefits for both banks and customers replacing the classic banking systems. An important issue of that is to understand what factors will impact the decisions of customers in adoption the service. This study examines how factors affecting adoption of Internet banking and the sequence in the banking system. The survey was conducted among Greek customers and resulted in 100 questionnaires. Among the factors that examined are the age, the education level and monthly income which are analyzed through econometric models. In addition the survey consists also with open ended-questions which examine the reliability, the efficiency and the security that the customers feel using Internet banking. The research`s results conclude that monthly income is a significant factor that can affect customer`s decision on using e-banking. Moreover, although the implications about the uncertainty of Internet banking are many the majority of the sample agree that there is sufficient reliability, efficiency and security among online transactions. Further investigations needs to be done for other factors that affect the adoption of Internet banking and among different places with different scales of economy.