The stabilities of cobweb models play an important role in economics. For investigating the global stability of two nonlinear cobweb models, we established some results on the stability of a first-order nonlinear difference equation for all initial values in an interval. We applied these results to the cobweb models studied in this paper. The equilibrium of one of the models is global stability if it is locally stable. The conditions of stability of the other model were given. In conclusion, the two cobweb models are globally stable under some conditions and these models can be used in research practice.