Current and traditional methods of load shedding are based on threshold values of frequency and voltage; thus, when the power system falls below these values, some mechanical control actions are activated as countermeasure against stability problems. Nevertheless, in many cases the traditional mitigation methods based on load shedding cannot ensure that the network remains in continuous operation after the presence of suddenly and severe perturbations. In addition, the development of control systems of wide area based on PMU’s measurements has allowed the development of different kinds of indices for the stability prediction. Thus, on-line diagnosis of the power system about angular stability and voltage stability gives better information about the system’s situational awareness. This paper proposes a methodology that allows the system operator to take a decision if applying the load shedding as a countermeasure for system instabilities caused by severe contingencies. In addition, the methodology identifies which are the nodes where the load shedding must be applied and the quantity of load shedding to be applied. The proposed load shedding methodology is based on a fuzzy logic decision method using the stability prediction index (SPI) and fast voltage stability index (FVSI). These indices can be computed on-line and they give the stability status of several operating areas. The methodology is tested on the NYPP-NETS of 68 nodes and it is illustrated with a cascade.