The electric power system is a complex nonlinear system that functions in a dynamic envi- ronment and is frequently subjected to a wide range of small and large disturbances. Small disturbances occur continuously due to load changes, while large disturbances are often caused by faults (such as equipment malfunction, human error, or attacks) and then propagate through the system. Such disturbances can lead to stability issues and, in the worst case, to blackouts. This thesis aims to tackle power system stability concerns by creating real-time detection al- gorithms that rely on Phasor Measurement Units (PMUs). These algorithms serve as early warning systems and are valuable inputs for stabilizing control techniques. The algorithms in question focus on two types of stability issues: short-term oscillatory stability, which pertains to low-frequency interarea oscillations, and long-term voltage stability, which is related to gradual voltage collapse. The first section of this thesis covers Low-Frequency Oscillations (LFO). While typically well-damped, under-damped LFOs can pose a significant threat to the grid’s stability, making it crucial to detect them early for real-time monitoring. An important aspect of analyzing oscillatory stability is determining the frequency and damping of critical oscillatory modes, which can be challenging due to closely spaced and noisy natural modes in PMU signals. To address this issue, the thesis proposes a method for detecting LFO using the Empirical wavelet transform, which adaptively extracts different signal modes through a wavelet filter bank. The second part of the thesis focuses on long-term voltage stability (LTVS) in electric power systems, which can gradually deteriorate over time due to the grid’s inability to meet demand. Factors such as insufficient reactive resources, load characteristics, and tap changer response can contribute to LTVS, but the thesis primarily examines the stressed power system caused by high active power demand from excessive load. For the real-time assessment of long-term voltage stability (LTVS), this study proposes an approach that utilizes data mining and ma- chine learning methods to evaluate long-term voltage stability (LTVS). The proposed technique employs a feature ensemble method to predict the voltage stability margin (VSM).