The invention relates to a mobile radio system having a plurality of mobile terminals (ME) connected with a mobile switching center (MZ) via an air interface for communication control and optionally for billing. The mobile terminals (ME) are controlled by a subscriber identity module (SIM) in which data for associating at least one user are stored, the subscriber identity module (SIM) having an identity (IMSI) associated therewith. For utilizing a mobile radio device for different purposes, such as private and business, a subscriber identity module is known which contains at least two permanently stored identities and thus has the disadvantage of being inflexible. The invention therefore proposes a subscriber identity module (SIM) containing a calculation rule for calculating from the stored identity (IMSI) at least one further identity (IMSI_w), the identities generated by the calculation rule being associated accordingly in the mobile switching center (MZ).