This thesis concerns the development of methods that can provide, in realtime, an early warning for an emerging blackout in electric power systems. The blackout in E-Denmark and S-Sweden on September 23, 2003 is the main motivation for the method development. The blackout was caused by occurrence of two severe system disturbances within a time interval of five minutes. Following the second disturbance where initial oscillations had damped out, a period of approximately 80s with slowly decaying voltage magnitude was observed, before a system blackout was experienced. It was of interest to develop methods, that could, in such situations, give an early warning for the emerging blackout. After investigation of data and plots taken from the time of the blackout, it was decided to focus the development on assessment of aperiodic small signal stability. In order to assess the system generators aperiodic small signal stability, expressions for stability boundaries were algebraically derived in the injection impedance plane. A method for detecting aperiodic small signal stability was established, which was based on one of the derived boundaries. The method carries out an element-wise assessment of the system aperiodic small signal stability where each generator is assessed specifically by using the value of its injection impedance and its corresponding system Thevenin impedance. For the purpose of obtaining distance-to-instability information, the generators operating point were visualized in the injection impedance plane. A mapping of the different operating points into a normalized injection impedance plane was derived, which enabled a visualization of multiple operating points on the same screen. Such visualization provides system operators a new mean of graphically assessing the system conditions in respect of aperiodic small signal stability and enables a quick identification of critical generators. The assessment method was implemented in an algorithm, that could effectively determine the required information for carrying out the stability assessment. The algorithm received a PMU-snapshot of the system conditions as an input and determined the injection and Thevenin system impedances I for all system generators. A test bench software was written for the purpose of testing the developed algorithm. A large scale test of the assessment method was carried out where a simulation of the blackout in E-Denmark and S-Sweden September 23, 2003 was used as a test case scenario. The simulation results were used to generate a synthetic PMU-snapshots of the system conditions which were used as an input to the assessment algorithm. The test results showed that the loss of aperiodic small signal stability of one machine was detected approximately 54s before the simulated blackout was experienced. The developed assessment method was therefore capable of providing, in real-time, an early warning for the occurrence of the emerging simulated blackout almost a minute before it occurred.