Abstract: Interface apparatus for connection between a data handling device and a data communication medium to enable data to be transferred between the device and the medium, is constituted, inter alia, by a data alignment device (7, 8) coupled in use to the data handling device. A memory (5, 6) is coupled for data transfer to the data alignment device (7, 8) and includes a number of substantially identical subsidiary, First-In-First-Out (FIFO) memories arranged in parallel. The number of subsidiary memories is chosen such that their overall width is at least equal to the longest length of data to be transferred between the memory (5, 6) and the alignment device (7, 8) in a single transfer step and the width of each subsidiary memory is equal to the shortest length of data to be transferred between the memory and the alignment device in a single transfer step.