The process is characterized in that it comprises: a step of reading tags recorded together with the packets, these tags defining the instants of arrival of the data packets to be recorded, on the basis of a tagging clock (8), a step of comparing the tags with values counted (9) on the basis of a transfer clock (8) for determining the instants of transfer on the bus of the data read from the record carrier, the frequencies of operation of the said tagging and transfer clocks being such that the maximum deviation between these frequencies, added to the maximum drift of the MPEG system clock, is, in proportion to the nominal values, of the order of or less than the drift of the system clock specified in the standard. Application to the storage of MPEG data.