The microscopic dynamics for the gel and liquid-crystalline phase of highly aligned D2O-hydrated bilayers of 1-palmitoyl-oleoyl-sn-glycero-phosphocholine (POPC) were investigated in the temperature range from 248 to 273 K by using incoherent quasi-elastic neutrons scattering (QENS). We develop a model for describing the molecular motions of the liquid phase occurring in the 0.3 to 350 ps time range. Accordingly, the complex dynamics of hydrogen are described in terms of simple dynamical processes involving different parts of the phospholipid chain. The analysis of the data evidences the existence of three different motions: the fast motion of hydrogen vibrating around the carbon atoms, the intermediate motion of carbon atoms in the acyl cha...