The invention relates to a cellular digital mobile radio system including base stations (B.sub.m, B.sub.n) and mobile stations (MS.sub.1, MS.sub.2) with transmitters and receivers. The invention also relates to a method of transmitting message information digitally between mobile and base stations in such a system. In accordance with the invention, at least two base station transmitters (B.sub.ma, B.sub.mb, B.sub.na, B.sub.nb) at a given transmitting distance from each other are assigned to each of certain cells (C.sub.m, C.sub.n) within a restricted geographical area. The base station transmitters which are assigned to the same cell transmit digitally modulated radio signals within the same frequency range at least partially simultaneously to the mobile stations of the cell. The radio signals from different base station transmitters associated with the same cell are digitally modulated with the same message information to the mobile stations in the cell. Different base station transmitters (9A, 9B) preferably transmit the digitally modulated radio signals with the same message information to a given mobile station with a given mutual transmission time shift. Here, the transmission time shift is selected individually for each mobile station, such that corresponding digitally modulated radio signals with the same message information to a given mobile station from different base station transmitters arrive practically simultaneously at the mobile station.