A method for transmitting data from a local radio network in a building to a remote center, in which the data are transmitted from terminals to data collectors installed in the building, and transmitted further from the data collectors to the center, where the data of the terminals are stored, wherein a) data telegrams with the data of the terminal, which were unidirectionally transmitted by a terminal in a radio communication of the local radio network, are received by a data collector installed within the radio range of the terminal, b) the data collector relays the data to the center via a mobile radio communication link, provided a mobile radio data transmission with the center comes about via the mobile radio communication link, wherein a connection setup from the data collector to the center via the mobile radio communication link is checked by the data collector, characterized in that the data collector is battery operated, that the terminals transmit sequential data telegrams in a transmission cycle with an average cycle time t z, and the data telegrams of terminals are received by the data collector in a combined asynchronous and synchronous reception, - wherein the data collector opens an asynchronous reception time window in a first regular cycle, the duration of which is timed in such a way that several data telegrams of a terminal can be received for the defined transmission cycle, and in which all data telegrams transmitted and receivable within the radio range in the period of the asynchronous reception time window are received, and - wherein the data collector opens a synchronous reception time window in a second regular cycle, in which the data telegram of a selected terminal is received, and whose duration is timed in such a way that the data telegram can be received despite a random fluctuation of the average cycle time t z, that the data collector as a data collector without mobile radio data transmission switches to a repeater function if a mobile radio data transmission with the center does not come about via the mobile radio communication link, and again unidirectionally transmits data telegrams received by terminals via radio communication of the local radio network, so that the data telegrams can be received by adjacent data collectors within the radio range of the data collector that is again transmitting the data telegrams, and relayed to the center, and that data telegrams are again transmitted via the repeater function of the data collector in the transmission cycle of the terminals. a) data telegrams with the data of the terminal, which were unidirectionally transmitted by a terminal in a radio communication of the local radio network, are received by a data collector installed within the radio range of the terminal, b) the data collector relays the data to the center via a mobile radio communication link, provided a mobile radio data transmission with the center comes about via the mobile radio communication link, the data collector is battery operated, that the terminals transmit sequential data telegrams in a transmission cycle with an average cycle time t z, and the data telegrams of terminals are received by the data collector in a combined asynchronous and synchronous reception, - wherein the data collector opens an asynchronous reception time window in a first regular cycle, the duration of which is timed in such a way that several data telegrams of a terminal can be received for the defined transmission cycle, and in which all data telegrams transmitted and receivable within the radio range in the period of the asynchronous reception time window are received, and - wherein the data collector opens a synchronous reception time window in a second regular cycle, in which the data telegram of a selected terminal is received, and whose duration is timed in such a way that the data telegram can be received despite a random fluctuation of the average cycle time t z, - wherein the data collector opens an asynchronous reception time window in a first regular cycle, the duration of which is timed in such a way that several data telegrams of a terminal can be received for the defined transmission cycle, and in which all data telegrams transmitted and receivable within the radio range in the period of the asynchronous reception time window are received, and - wherein the data collector opens a synchronous reception time window in a second regular cycle, in which the data telegram of a selected terminal is received, and whose duration is timed in such a way that the data telegram can be received despite a random fluctuation of the average cycle time t z, that the data collector as a data collector without mobile radio data transmission switches to a repeater function if a mobile radio data transmission with the center does not come about via the mobile radio communication link, and again unidirectionally transmits data telegrams received by terminals via radio communication of the local radio network, so that the data telegrams can be received by adjacent data collectors within the radio range of the data collector that is again transmitting the data telegrams, and relayed to the center, and that data telegrams are again transmitted via the repeater function of the data collector in the transmission cycle of the terminals.