A modem relay connection or other type of connection established between terminals of a communication system includes a series arrangement of multiple modems or other data communication devices. The connection includes two endpoint data communication devices, and at least one non-endpoint data communication device within the serial arrangement between the two endpoint devices. Each of the endpoint data communication devices may have a first type of escape to on-line command mode feature, and the one or more non-endpoint data communication devices are configured so as to have a second type of escape to on-line command mode feature different than the first type of escape to on-line command mode feature. This ensures that entry of the on-line command mode by one of the endpoint devices will not inadvertently disrupt the desired operation of the one or more non-endpoint devices. A given non-endpoint device may be configured to have the escape to on-line command mode feature of the second type by, e.g., altering a command structure of the non-endpoint device, or by appropriate modification of software which detects an escape sequence.