The present invention presents a solution for limiting access rights in a building, which building contains a conveying system, an access control system connected to the conveying system, which access control system comprises at least one short-range identification point and at least one long-range identification point and in which access control system passengers have a personal terminal device for giving service requests to the conveying system. A terminal device is taken into the operating area of a short-range identification point, the access rights connected to the service requests of the terminal device are activated, the terminal device is taken into the operating area of a long-range identification point and a service request generated with the terminal device is transmitted to the conveying system, if the access right connected to the service request is valid on the basis of the activation.