Determination of the loadability margin for various security limits is of great importance to the secure operation of the power system as is proposing a reliable method for the fast determination of bifurcation points in the systems. Eigenvalue calculation is normally used for both actions. Whereas this method is computationally expensive, soft computing methods are employed to improve calculation time. In this paper a support vector machine (SVM) method is proposed to aid the fast classifying of bifurcation stability of the system. A novel approach based on particle swarm optimization (PSO) is also introduced to find the closest load ability margin and its corresponding loading direction. Three security limits are considered in this study: Saddle-node bifurcation, limit-induced bifurcation, and Hopf bifurcation. The simulation results for two test systems demonstrate the effectiveness of the proposed methods.