Gigahertz Peaked Spectrum (GPS) sources form a key element in the study of the onset and evolution of radio-loud AGN, since they are most likely the young counterparts of extended radio sources. Here we discuss space-VLBI observations of GPS sources, which enable us to obtain unprecedented angular resolution at frequencies near their spectral turnovers. Observed peak brightness temperatures of Log[T]=10.5-11 Kelvin indicate that synchrotron self absorption is responsible for their spectral turnovers. This is in close agreement with previous size - spectral turnover statistics for GPS sources. The combination of these new space-VLBI observations with ground-based VLBI observations taken at an earlier epoch, confirm the young ages for the most compact GPS galaxies of several hundred years.