Abstract: The process is characterized in that, if: DTS_next_AUold−PCRold<DTS_first_AUnew−PCRnew, then, in a first step, the data of one or more last images of the old stream and/or one or more first images of the new stream are replaced by data of one or more new pre-encoded images of which the number is smaller so that the new value of PCRold and/or PCRnew thus obtained satisfies the relation: DTS_next_AUold−PCRold≧DTS_first_AUnew−PCRnew, in a second step, TS stuffing packets are inserted between the point of exit and the point of entry so as to make the decoding instants DTS_next_AUold and DTS_first_AUnew coincide. Applications relate to the transmission and storage of programs, as well as to the insertion of advertisements or to regional or local handover.