A first data flow (DS1) for a first data transmission system (DÜ1) with a first data rate contains ATM data cells (2, 3, 4) and structure data (10, 11, 12) allocated to a section (13) consisting of several ATM cells and divided and spaced out according to predetermined instructions. The data flow (DS1) is converted, while retaining its ATM data cell format, into a second data flow (DS2) containing only ATM data cells for a second data transmission system (DÜ2) with a second, higher data rate. Here, the structure data (10, 11, 12) are separated from the first data flow and entered into a marked structure cell (64) with an ATM data cell format for the section concerned. The structure cell (64) is inserted into a second data flow (DS2) so as partly to fill an unoccupied section resulting from the differing data rates.