Finding DC operating points of nonlinear circuits is an important and difficult task. The Newton-Raphson method adopted in the SPICE-like simulators often fails to converge to a solution. To overcome this convergence problem, homotopy methods have been studied from various viewpoints. However, most previous studies are mainly focused on the bipolar transistor circuits and no paper presents the global convergence theorems of homotopy methods for MOS transistor circuits. Moreover, due to the improvements and advantages of MOS transistor technologies, extending the homotopy methods to MOS transistor circuits becomes more and more necessary and important. This paper proposes two nonlinear homotopy methods for MOS transistor circuits and proves the global convergence theorems for the proposed MOS nonlinear homotopy method II. Numerical examples show that both of the two proposed homotopy methods for MOS transistor circuits are more effective for finding DC operating points than the conventional MOS homotopy method and they are also capable of finding DC operating points for large-scale circuits.