This article reviews our THz-spectroscopy results on the intra-excitonic transitions of different III-V multi quantum well structures. Following a brief introduction to THz Time-Domain Spectroscopy a detailed description to the data analysis and extraction of refractive index and absorption is given. The behavior of the induced excitonic THz absorption in GaAs/(AlGa)As and (GaIn)As/GaAs multi quantum well structures is compared. Good agreement with previous experiments on the GaAs/(AlGa)As system [1,2] is obtained. A distinctly different behaviour is observed for the (GaIn)As/GaAs structures.