A method and control device for controlling the display of multimedia data on an audio-video rendering device, e.g. a TV device (AVD), when a channel selection navigation, from a first channel to a second channel, is activated. It is controlled which, how and when particular multimedia data is displayed as it may for instance be necessary to perform parental control to prevent the display of “adult” multimedia data at particular times of the day, or advertisements at times when they could disturb the comfort of watching of the user of the TV set. In a preferred embodiment, multimedia data of a second content type, e.g. “normal” programs (PGS) or previews of programs (PRS) is displayed in replacement of the advertisements during a predetermined time delay called advertisement-play grace period.