The stability limits in binary fluid mixtures are investigated on the basis of the global phase diagram approach employing a model for the attracting hard-sphere fluid. In addition to the diffusion spinodals the mechanical spinodals are included. As a result one finds topologically different types of the diffusion spinodals while only one shape exists for the mechanical spinodals which are present in the region of liquid-vapor equilibria only. The diffusion spinodals represent the underlying properties of the phase behavior. The types of stable phase behavior therefore resemble that of the spinodal behavior. The different shapes of the spinodals can be important for nonequilibrium processes in nature and technology.