Abstract This thesis presents computational studies of both the static and dynamic parameters of the nuclear magnetic resonance (NMR) spectroscopy of gaseous xenon. First, state-of-the-art static magnetic resonance parameters are computed in small xenon clusters by using methods of quantum chemistry, and second, time-dependent relaxation phenomena are investigated via molecular dynamics simulations at different experimental conditions. Based on the underlying quantum and classical mechanics concepts, computational methods represent a procedure complementary to experiments for investigating the properties of atoms, molecules, clusters and solids. Static NMR spectral parameters, chemical shift, shielding anisotropy and asymmetry parameter, nuclear quadrupole coupling, and spin-rotation coupling, are calculated using different electronic structure methods ranging from the uncorrelated Hartree-Fock method to correlated second-order Møller-Plesset many-body perturbation, complete/restricted active space multiconfiguration self-consistent field, and to coupled-cluster approaches. The bond length dependence of these properties is investigated in the xenon dimer (Xe2). A well-characterized property in experimental NMR, the second virial coefficient of nuclear shielding, is theoretically calculated by a variety of methods and convincingly verified against experimental findings. Here, it is mandatory to include effects from special relativity as well as electron correlation. As a side result, a purely theoretical potential energy curve for Xe2, comparable to best experimental ones, is calculated. A pairwise additive scheme is established to approximate the NMR properties in differently coordinated sites of xenon clusters Xen (n = 2 - 12). Especially the pairwise additive chemical shift values are found to be in close agreement with quantum-chemical results and only a small scaling factor close to unity is needed for the correct behavior. Finally, a dynamical magnetic resonance property, the experimental nuclear spin-lattice relaxation rate R1 of monoatomic Xe gas due to the chemical shift anisotropy (CSA) mechanism is validated from first principles. This approach is based on molecular dynamics simulations over a large range of temperatures and densities, combined with the pairwise additive approximation for the shielding tensor. Therein, the shielding time correlation function is seen to reflect the characteristic time scales related to both interatomic collisions and cluster formation. For the first time, the physics of gaseous xenon is detailed in full in the context of CSA relaxation.