A communications port of a network communications device maintains capability information indicating that under normal operating conditions a communications link is capable of operating in a secure mode in which communications signals of the communications link are unintelligible to an intruder having an unauthorized physical connection (e.g. tap) to the communications link. During operation, the port detects occurrence of a link event of a type that can invoke an automatic communications-mode control mechanism to change the operating of the communications link to a non-secure mode in which communications signals of the communications link are intelligible to such an intruder. An example is Ethernet auto-negotiation which can change from relatively secure 1000BaseT signaling to relatively non-secure 10/100BaseT signaling. Based on the capability information, the port responds to the link event by preventing the automatic communications mode control mechanism from changing the operating of the communications link to the non-secure mode.