With the time-integrated measurements in the previous chapter, we obtained a detailed image of the longitudinal-lateral mode structure, and observed the interplay of various gain dynamics, such as mode clustering and hole burning effects. In the following, we study the time-dependent dynamics of the longitudinal-lateral modes, which is closely coupled to the lateral carrier dynamics. First, we focus on the effects at pulse onset and later on mode competition. With a rate equation based simulation approach, we are able to closely investigate the relevant processes and study the stability of mode competition across a wide parameter range.