Oscillations in power systems are a common problem that cause wear and decreased electric power quality. Hence, it is of great importance to detect when oscillations occur and to analyze which machines that are involved. This master thesis was a pre-study to implement an application that can detect and analyze power system oscillations in the real-time interactive simulator ARISTO, which is a simulator that the authority responsible for the transmission system of Sweden, Svenska kraftnät, develops. The working process included a literature study which resulted in several methods that were selected for deeper analysis. The theory of oscillation detection is called spectral analysis. To analyze which machines that are involved in the oscillations, phase shift calculations are required. The study showed that the methods ESPRIT (estimation of signal parameters via rotational invariant techniques) and Capon performed the most accurate results in the spectral analysis. Among the selected methods for phase shift calculations, the discrete Fourier transform obtained the most accurate results. Among the scientific reports and publications that discussed power system oscillations, the method GPOF (generalized pencil-of-function method) was most frequently used. The reason for this depends on the method's unique property to calculate damping, which can be a crucial aspect to analyze in power systems. This master thesis has examined several other methods that yield more accurate results in terms of spectral analysis and phase shift calculations. However, in contrast to GPOF, those methods cannot calculate the damping of the system which can be a substantial drawback.