Abstract: A method and circuit arrangement for connecting ATM communication equipment to an ATM trunk group, where characteristic parameters reported for virtual connections to be set up are allocated to connection classes and to transmission classes corresponding to the connection classes. The parameters are defined for the individual lines of the ATM trunk group. Further, line particulars with respect to all of the transmission classes for which a virtual connection can still be set up, based on currently available free transmission capacity, are individually retained for the associated individual ATM trunks. When a request for setting up a virtual connection is present, an individual trunk for setting up the virtual connection is selected during the course of a search event involving the line particulars of all individual trunks. A transmission class that corresponds to the connection class to be considered in the virtual connection to be set up is determined from the line particulars of the individual trunk.