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The present work investigates the numerical evolution of linearized oscillations of non-rotating, spher-ically symmetric neutron stars within the framework of general relativity. We derive the appropriate equations using the (3+1)-formalism. We first focus on the evolution of radial oscillations, which do not emit gravitational waves. The associated system of equations being quite simple, we demonstrate how to handle a numerical instability that also occurs in the non-radial case, when the stellar model is constructed based on a realistic equation of state. We devise a coordinate transformation that not only removes this instability but also provides much more accurate results. For comparison reasons, we com-pute the eigenfrequencies of the radial modes with an eigenvalue code and thereby confirm the results of Väth & Chanmugam, which differ from previous calculations that were performed by Glass & Lindblom. The main part deals with the evolution of non-radial oscillations (l ≥ 2) of neutron stars. Here, we compare different formulations of the equations and discuss how they have to be numerically dealt with in order to avoid instabilities at the origin. We present results for various polytropic stellar models and different initial data. They show that the quasi-normal modes of the star, such as the f-, the p-, and thew-modes, can, indeed, be excited by suitable initial data. However, the excitation strength of the w-mode