Optical bistable behavior for a system of inhomogeneously broadened two sorts of twolevel atoms in a ring cavity is investigated outside the rotating wave approximation (RWA). The model Maxwell-Bloch equations are treated with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or mushroom bistability simultaneously with bi-and double-bistability in the fundamental field component. Inhomogeneous broadening and transverse field effects are also considered.