- / An amorphous system can be viewed as a point in con guration space spending most of its time vibrating about local minima of the energy hypersurface. Transitions to adjacent minima, which correspond to elementary events of structural rearrangement, are rare, since the vibrational energy of the system is not high enough to overcome the surrounding energy barriers. Therefore, molecular dynamics simulations, which can track a system's behavior over at most a few nanoseconds, fail to give us information about the atomistic nature and characteristics of such minimum-to-minimum transitions. In this work we try a di erent approach: we construct molecular con gurations of an amorphous Lennard-Jones solid, which, for given values of the temperature and stress/pressure, constitute local minima of the free energy under the quasi-harmonic approximation (QHA). From the volumetric behavior of these con gurations for various values of the temperature and/or pressure we conclude that the QHA is very reasonable for our system and we calculate the values of the isothermal compressibility and of the elastic constants. We then identify representative paths in con guration space leading from one free energy minimum to an adjacent one at xed temperature and pressure. For each of these transitions or elementary structural relaxation events we determine the corresponding rate constant using the principles of multidimensional transitionstate theory. The distribution of free energy barriers is found to be strongly asymmetric and extremely broad, whereas the corresponding distribution of activation entropies is narrow. There is a strong positive correlation between the volume change and the free energy change accompanying each of these elementary transitions, as would be expected from observed volume relaxation phenomena in glasses. The physical phenomenon of physical ageing can be described as a sequence of elementary relaxation events. Therefore, our next step is the analysis of sequential minimum-to-minimum transitions. This analysis is performed via a novel kinetic Monte-Carlo simulation method, which we call quasi-MD. The quasi-MD method tracks di erent stable initial con gurations "escape" through one of the transition states surrounding their current minimum and get trapped inside a neighboring one, which becomes the new current state for the system. Each of the observed transition events is associated with a characteristic time related to the randomly chosen escape route, integrating-out the vibration inside the minimum. This way, it is possible to follow the time-dependence of the system's properties during the relaxation process. One of the most characteristic such properties for the phenomenon of physical ageing is the self-part of the intermediate scattering function Ss(q; t). Calculation of the timedependence of Ss(q; t) for the glassy Lennard-Jones using quasi-MD clearly shows the three known characteristic regions: a) initial rapid decay which corresponds to local motion of the particles within their "cage", b) the slowly decaying plateau region corresponding to relaxation of the "cage", called the -relaxation, and c) the nal decay which corresponds to the breakup of the "cage" and escape of the particles, designated as the -relaxation. The glassy Lennard-Jones system used so far is an ideal system for the development of novel simulation methods and the analysis of the validity of di erent approaches. However, more complex systems are interesting from a technological point of view. Therefore, our nal step is the analysis of a glassy polymer. We focus on the validity of the QHA in glassy atactic polypropylene. Following the same procedure as in the case of Lennard-Jones spheres, we construct di erent stable amorphous con gurations for a series of temperatures and pressures. Using these con gurations we calculate the values of the thermal expansion coefficient and isothermal compressibility, which agree reasonably well with available experimental data. Finally, the amorphous polypropylene con gurations get uniaxially strained leading to the estimation of the value of Young modulus.