With two waves incident on a two-dimensional (2D) nonlinear superlattice, the relation between ψ, and the output intensities is bistable. Here, the ψ is the relative phase between the two waves. That is to say, as ψ is slowly varied within one cycle, a hysteresis loop in the ψ-output relation can be traced out. A very low threshold power is required in an appropriate 2D nonlinear superlattice for the optical bistability.