A data stream multiplexing apparatus having a stream modifier for producing modified sub-picture data stream from a sub picture data stream where a first sub-picture data unit containing pixel data forming a sub-picture image with a preset display time period is located along a time axis by additionally locating at least one of second sub-picture data unit having almost same contents as the first sub-picture data unit within the display time period of the first sub-picture data unit on the sub-picture data stream, and a multiplexer responsive to input modified sub-picture data stream produced by the stream modifying means and other data streams reproduced in synchronous with the modified sub-picture data stream, for multiplexing these streams after packetizing them by a prescribed length.