A computer system with a mode switching function capable of discriminating a DTMF signal serving as a mode selection signal and supporting a variety of communication services in accordance with the mode selection signal. The computer system includes a main computer unit for executing computer computation function and supporting a variety of communication services such as an automatic answering service, a facsimile communication service, a data communication service, a visual communication service and the like, a modem and an automatic answering unit. The main computer unit has a system bus, a storage device including a memory connected to the system bus for storing service application programs and data, and a central processing unit (CPU) connected to the system bus for executing computer computation function and executing the service application programs capable of supporting the variety of communication services. The modem which is an interface device coupled between the main computer unit and a telephone line for permitting the exchange of digital data with the remote communication terminal, such as a telephone, an automatic answering machine, a facsimile machine, a modem-supported computer, a visual communication machine or the like, over the telephone line by providing an interface function between each terminal and the telephone network.