An advanced time-domain dynamical model for the investigation of semiconductor optical amplifiers (SOA) is presented. The model accounts for the ultrafast gain dynamics, the gain saturation and the gain spectral profile. It is also suitable for analyzing the amplifier in a system environment. As an example the model is used to investigate the gain dynamics of an SOA as well as the characteristics of an interferometer switch semiconductor laser amplifier in a loop mirror (SLALOM). Good agreement between modeling and experiment is shown. The model can be applied to the investigation of other optically time-division multiplexed (OTDM) applications, too.