The response kinetics of liquid crystalline phosphatidylcholine bilayer stacks to rapid, IR-laser-induced temperature jumps has been studied by millisecond-time-resolved X-ray diffraction. The system reacts on the fast temperature change by a discrete bilayer compression normal to its surface and a lateral bilayer expansion. Since water cannot diffuse from the excess phase into the interbilayer water region within the 2 ms duration of the laser pulse, the water layer has to follow the bilayer expansion, by an anomalous thinning. Structural analysis of a 20 ms diffraction pattern from the intermediate phase indicates that the bilayer thickness remains within the limits of equilibrium values. Both, the intermediate structure and its relaxation into the original equilibrium L-alpha, phase, depend on the viscoelastic properties of the bilayer/water system. We present an analysis of the relaxation process by an overdamped one-dimensional oscillation model revealing the concepts of Hooke's law for phospholipid bilayers on a supramolecular basis. The results yield a constant bilayer repulsion and viscosity within Hooke's regime suggesting that; the hydrocarbon chains act as a buffer for the supplied thermal energy. The bilayer compression is a function of the initial temperature and the temperature amplitude but is independent of the chain length.