A data processing apparatus, such as a facsimile apparatus, connected to a LAN, that transmits and/or receives data to or from another apparatus, wherein even if an error or failure such as a printer error or an insufficiency of available space in image memory for storing image data occurs, the required process is continued by transferring the image data from the data processing apparatus to another apparatus also connected to the LAN. The data processing apparatus has the capability of detecting an error in the LAN when the apparatus is connected to the LAN. This allows the data processing apparatus to operate correctly without problems that might otherwise occur due to the error in the LAN. The data processing apparatus also has the capability of operating in an adequate process mode corresponding to a process command contained in a received packet. This allows effective use of the data processing apparatus.