When a liquid is cooled to produce a glass, its dynamics, dominated by the structural relaxation, slows down dramatically, becoming of ≈100 s at the glass-transition temperature, Tg. At a slightly higher temperature (≈1.2Tg), a second, faster process, known as Johari-Goldstein (βJG) decouples from the structural one and remains active even in the glassy-state. It is nowadays established that the βJG -process is deeply connected to the structural one, though its microscopic origin and its role in the glass transition are still under debate. In this Thesis the spatial and temporal properties of the atomic motions within the JG-relaxation are investigated in two mono-hydroxyl alcohols using the technique known as nuclear γ-resonance time-domain interferometry (TDI). The results here obtained show that, within the βJ-relaxation, about one molecule out of four undergoes a restricted dynamics characterized by displacements of the order of 10% of the average inter-molecular distance. These re-arrangements correspond to local cage-breaking events and such un-caged molecules form a percolating cluster within the sample. At the same time we also found evidences of larger re-arrangements, occurring at a longer timescale with respect to the cage-breaking events and reaching out at least to the inter-molecular length-scale.