A communication system performs, by first and second data processing apparatuses, an electromagnetic-induction communication using a carrier having a single frequency. A transfer rate for use between the first and second data processing apparatuses is changeable in one transaction. The first data processing apparatus determines whether a transfer rate can be changed based on data transmitted from the second data processing apparatus. When the first data processing apparatus determines that the transfer rate can be changed, the first data processing apparatus transmits to the second data processing apparatus a request to change the transfer rate to one of a plurality of transfer rates.