A radio communication system, for example a TDMA/CDMA radio communication system, has at least one base station recurringly offering frequency channels for a random access for mobile stations in an upstream direction. The mobile station that requests a connection setup measures a reception power of a signal sent in a downstream direction by the base station and sets a transmission power for sending an access radio block to the base station dependent on the measured reception power. A variable transmission power control can thus be implemented at the mobile station side with the assistance of the measured reception power of the signal transmitted on the part of the base station, being also capable of being implemented for random access of the mobile stations, this having previously always occurred with maximum transmission power.