A mobile radio telephone system has at least one first radio cell, several radio cells to that are adjacent to the first radio cell and base stations, each of the latter covering one of the radio cells. A sub-group of the adjacent radio cells is determined depending on the position of a mobile station in the first radio cell. The mobile station subsequently measures a quality parameter of only those signals of the base stations associated with the sub-groups of the adjacent radio cells. One possible advantage is that the time required to carry out the measurements is relatively short as a result of the reduction of their number.