We present analytical considerations of "self-mode-locked" operation in a typical vertical external-cavity surface-emitting laser (VECSEL) cavity geometry by means of Kerr lens action in the semiconductor gain chip. We predict Kerr-lens mode-locked operation for both soft- and hard-apertures placed at the optimal intra-cavity positions. These predictions are experimentally verified in a Kerr-lens mode-locked VECSEL capable of producing pulse durations of below 500 fs at 1 GHz repetition rate.