Upgraded requirements for data integrity and data efficiency in real-time process control applications necessitate critical investigations on existing standard data transmission conventions such as the HDLC (high level data link control) protocol. It is shown that a single bit error within an ordinary HDLC frame may cause an undetectable message error at the receiver. Further proposals for using modified HDLC protocols which guarantee the detection of single bit errors fail to detect double bit errors within a frame. Refined assessments for corresponding nondetectable message error probabilities are based on bit sequence probabilities in HDLC frames which differ slightly from bit sequences in original text fields due to the `bit escaping mechanism' required by the HDLC protocol.