1. A data communication apparatus having an on-line mode and an off-line mode and being capable of parallel operation of the on-line mode and the off-line modes, comprising: display means for changeably displaying an on-line operation state and an off-line operation state of the apparatus; detection means for detecting that the data communication apparatus has received a predetermined procedure signal; and control means for controlling to changeably display an on-line operation state and an off-line operation state on said display means, in accordance with a detecting result of said detecting means, wherein said control means changes the display to said off-line operation state display from said on-line operation state display before completion of data communication, in accordance with reception of the predetermined procedure signal.