In a facsimile apparatus provided with a facsimile modem function through which a personal computer performs communication, the changeover between a facsimile mode and a facsimile modem mode is made based on the setting and activation conditions of the apparatus. When a call comes in while the facsimile apparatus is in the facsimile modem mode, if no power is supplied to the personal computer, the operation mode is changed to the facsimile mode to receive the call. When the personal computer does not respond to a call notification although power is supplied thereto, a warning sound is provided. A call coming in when the facsimile apparatus is used as an image data inputting and outputting apparatus of the personal computer is ignored. The facsimile apparatus does not respond to an AT command received within a predetermined period of time after the setting of an original to be transmitted, so that the facsimile mode is maintained.