This paper presents a coevolutionary approachto analyzing supply function equilibrium (SFE) models of anoligopolistic electricity market. Both the affine supply functionmodel and the piece-wise affine supply function model are considered.Different parametrization cases of the affine supply functionmodel are analyzed. The piece-wise affine supply functions thathave a large number of pieces are used to numerically estimatethe equilibrium supply functions of any shapes. Simulation casesof the piece-wise affine supply function model with different peakloads, nonquadratic and nonconvex costs, and different demandelasticities are studied. An example based on the cost data fromthe real-world electricity industry is used to validate the approachpresented in this paper. Simulation results show that the coevolutionaryapproach rapidly converges to SFE in the affine supplyfunction model simulation and robustly converges to SFE in allcases of the piece-wise affine supply function model simulation.The approach is robust and flexible and has the potential to beused to solve the complicated equilibrium problems in real-worldelectricity markets.