A data processing system includes a wireless terminal and first and second
data processing apparatuses. The first data processing apparatus,
responsive to receiving from the wireless terminal data including
identification information identifying the second data processing
apparatus, sends to the second data processing apparatus a shift signal
for shifting the second data processing apparatus from a power saving
mode incapable of receiving wireless communication data to a standby mode
capable of receiving wireless communication data. Further, the second
data processing apparatus shifts from the power saving mode to the
standby mode responsive to receiving the shift signal from the first data
processing apparatus.