In September 1968 the University of Hawaii began work on a research program to investigate the use of radio communications for computer-computer and console-computer links. The report describes a remote-access computer system - THE ALOHA SYSTEM - under development as part of that research program and discusses some advantages of radio communications over conventional wire communications for interactive users of a large computer system. An analysis of the random access communication method used in THE ALOHA SYSTEM is provided and it is shown that the maximum number of interactive users who can be supported by the system is about 160.