as the adjusting commands are determined for controlling the matching operation for each antenna 2 because of the modular construction of the antenna system 1 the latter can be changed in a particularly simple manner in its arrangement for example the antenna system 1 can be reduced to a simple monopole antenna in that one of the two antennas 2 is deactivated for example by a switching off by means of the control 14 or by means of a disconnection from the matching module 8 according to the type and construction of the control unit 4 the respective matching module 8 may include a memory module 18 in addition or as an alternative preferably for various frequencies in the frequency range of from 2 to 30 mhz for example at a 5 mhz interval in each case the pertaining impedance values and the resulting required l c elements number and size are filed in the memory module 18 thus independently of the actual measuring of the input impedance of the respective antenna 2 the matching of the antenna 2 is automatically permitted for a given frequency fig4 shows a vehicle 18 with an antenna system 1 of the above described type in this case the antenna system 1 is arranged on a carrier element 20 which is fastened on the roof of the vehicle 18 according to the type and the construction of the antenna system 1 the respective modules are individually or jointly for example surrounded by a housing arranged on the carrier element 20 for example as illustrated in fig4.