The majority of normal disk galaxies are characterized by non-axisymmetric structures like spirals or bars. These structural elements have been widely discussed in the literature as a result of gravitational instabilities which are connected to growing density waves or global instabilities of disks. A first insight into the properties of galactic discs was provided by linear stability analysis. However, a disadvantage of linear stability analysis remained its restriction to small perturbations, both in amplitude and wavelength. Thus, numerical simulations, especially hydrodynamical and stellar-hydrodynamical simulations became a primary tool for the analysis of galactic evolution.