In a processor-controlled multimedia terminal connected to a processor-controlled multimedia docking device, a group of application programs is stored and made available for execution. The application programs can run on the multimedia terminal in the foreground or background. Only one application program of the group is executed in the foreground at one time. An application program can output data via a graphical user interface while running in the foreground. While running in the background, however, an application program cannot output data via the graphical user interface. In the multimedia terminal, a memory area is also provided, to which the application programs have read and write access during execution thereof. An application-specific data set is stored in the memory area for each application program, the data set remaining in the memory area even after the respective application program has ended. A first application program, during execution thereof in the multimedia terminal, reads the application-specific data sets of the other application programs of the group and stores them in a list. The list is also transmitted to the multimedia docking device. Data for the application programs contained in the list is displayed on the multimedia docking device. An application program is selected from the list as the second application program. A switchover is then made in the multimedia terminal from the execution of the first application program to an execution of the second application program by the multimedia docking device, wherein the execution of the first application program in the foreground on the multimedia terminal is ended and the second application program is brought to run in the foreground.