A subscriber station for a serial bus system is described. The subscriber station includes a communication control device for generating a message to serially transmit on the bus system, and/or for reading a message that has been serially received by the subscriber station on the bus system. The communication control device is configured to decide whether there exists, for aborting a serial transmission of the frame onto the bus line which is currently being carried out, an abortion criterion according to which a serial transmission of a higher-priority frame for a message is more important than the serial transmission of the frame onto the bus line which is currently being carried out, and to provide in the frame currently being serially transmitted, on the basis of the decision that has been made, a signalization as to whether or not the frame currently being serially transmitted is to be aborted.