During the last decade the decrease in the size of computing machinery, coupled with the increase in their computing power has lend to the development of the concept of mobile computing. Effects of this new vision is currently evident in the flourishing numbers of mobile telephones and portable computing units. In this paper we briefly investigate some issues concerning the security of mobile computing systems, within the framework of the categories of mobility, disconnection, data access modes and scale of operation (Imielinski & Badrinath, 1993). In contrast to previous works which concentrate on security in wireless communications, we focus on the security of interactions which are built upon the underlying wireless communications medium. Some conclusions are presented on the future directions for security research in mobile computing systems.