Packets of data, some of which may carry a timestamp value, are transmitted through an Asynchronous Transfer Mode (ATM) network. Prior to transmission, each packet of data is encapsulated in a respective convergence sublayer protocol data unit (CS-PDU) having a header portion and a payload portion. The header portion of each CS-PDU contains a time correction indicator (TCI), which indicates whether the CS-PDU carries a packet of data having a timestamp value that may require correction after the CS-PDU passes through the network, and a time reference correction (TRC) field. Each CS-PDU is then segmented into a plurality of successive segments; a first one of the segments of each CS-PDU contains the CS-PDU header. Each segment is then inserted into the payload section of a respective ATM cell for transmission through the network. At each node in the network, cells are examined to determine if they contain a CS-PDU header. If a cell contains a CS-PDU header, any variable delays imposed upon that cell as it passed through the node are measured and added to the TRC field in the CS-PDU header prior to sending the cell to the next node. At a destination node, the accumulated TRC value may be added to the time stamp value of the packet carried in the CS-PDU in order to compensate for the variable delays imposed upon that packet as the cells carrying the packet traversed the network.