An Internet facsimile communication method and an Internet facsimile machine wherein the Internet facsimile machine of the transmitting side shortens the time required from starting of the scanning of the original to be transmitted and receiving of the image data of the original at the terminal of the receiving side, until the completion of the processing such as printing or distributing of the image data. In one example, the Internet facsimile machine of the transmitting side is capable of transmitting, in still shorter period of time, the image data most appropriate to the ability of the Internet facsimile machine of the receiving side, and the Internet facsimile machine for carrying out this Internet facsimile communication method is provided. In another example, a communication system is provided for shortening the time until the delivery confirmation is replied, by replying the electronic mail of the delivery confirmation efficiently.