This paper is devoted to exploring the aperiodic and Oscillatory small signal stability boundaries in the space of power system parameters. In practical terms, they restrict the domain where all power system operating points must be kept for stable operation. In the proposed technique, to trace these boundaries, the saddle node and Hopf bifurcation points are computed along a given ray (loading direction) in the parameter space. By rotation of the ray, the entire boundaries are revealed. The bifurcation expressed in a plane provide a clear geometrical view of the stability constraints when a number of power system parameters are treated as variables. In the paper, particular attention is given to finding the initial guesses of unknown variables in the first step of the proposed technique, and to reliable and accurate tracing the boundaries in its second step. The corresponding numerical techniques, as well as examples of their application, are given.