We present radiative lifetime measurements of excited states in semiconductor self-assembled quantum dots. By increasing the photoexcitation intensity, excited-state interband transitions up to n=5 can be observed in photoluminescence. The dynamics of the interband transitions and the intersublevel relaxation in these zero-dimensional energy levels lead to state filling of the lower-energy states, allowing the Fermi level to be raised by more than 200 meV due to the combined large intersublevel spacing and the low density of states. The decay time of each energy level obtained under various excitation conditions is used to evaluate the intersublevel thermalization time. \textcopyright{} 1996 The American Physical Society.