Real-time coherent Grazing-Incidence Small-Angle X-ray Scattering was used to investigate the average kinetics and the fluctuation dynamics during self-organized ion beam nano-patterning of two semiconductor surfaces: silicon at room temperature and germanium heated above its recrystallation temperature. For silicon nano-patterning, initially flat samples at room temperature were bombarded by a broad collimated beam of 1keV Ar+ and Kr+ ions at 65° polar angle, leading to the amorphization of the ion-irradiated surfaces and the spontaneous formation of nanoscale ripples. The temporal evolution of the average X-ray scattering intensity shows the evolution of average kinetics, while the fluctuation dynamics can be investigated by correlation of X-ray speckles. The surface behavior at early times can be explained within a linear theory framework. The transition away from the linear theory behavior is observed in the dynamics since the intensity correlation function quickly evolves into a compressed exponential decay on length scales corresponding to the peak wavelength and a stretched exponential decay on shorter length scales. The correlation times for silicon nano-patterning are maximum at the ripple wavelengths while they are smaller at other wavelengths. This has notable similarities and differences with the phenomenon of de Gennes narrowing. Overall, this dynamics behavior is found to be consistent with the simulations of a nonlinear growth model by Harrison et al. Following the formation of self-organized nano-ripples, they move across the surface. Homodyne X-ray alone cannot detect the motion, but because of the gradient of ion flux across the sample, we were able to measure in-situ the corresponding ripple velocity gradient by cross-correlating speckles and tracking their movements. For germanium nano-patterning at an elevated temperature, flat germanium samples kept at 300°C were bombarded by 1keV Ar+ ions at normal incidence. Unlike the case when surfaces are amorphizated during room temperature bombardment, the crystalline nano-pattern formation occurs mainly due to a surface instability caused by the Ehrlich-Schwoebel barrier. By using a linear theory analysis on the X-ray scattering intensities in the early times, we measured the contribution of the Ehrlich-Schwoebel barrier to the crystalline nano-patterning kinetics.