Over the last years several experimental and theoretical studies of diffusion kinetics on the nanoscale have shown that the time evolution differs from the classical Fickian law (kc=0.5). However, all work was based on crystalline samples or models, so far. In this letter, we report on the diffusion kinetics of a thin amorphous-Si layer into amorphous-Ge to account for the rising importance of amorphous materials in nanodevices. Employing surface sensitive technics, the initial kc was found at 0.7+-0.1. Moreover, after some monolayers of Si dissolved into the Ge, kc changes to the generally expected classical Fickian law with kc=0.5.