The invention relates to a communications system and a method for establishing a broadband connection, for example a multi-media connection between two or more users, by means of exchanges in a communications network, for example an ATM network. According to the invention, when the exchanges receive a request from a calling user to establish a broadband connection, said exchanges first establish a minimal connection between the users and once the minimal connection is in operation between the users, the requested broadband connection is established. The users of broadband network capacities, which have been reserved by the network at the request of the user, are billed during the call phase. Broadband connections of this type can receive a higher priority than the upgrade of minimal connections to complete connections. A voice connection comprising audio data constitutes for example a minimal connection. The broadband connection takes place for example between video telephones.