Fast solvers for edge element discretizations of the time-harmonic Maxwell equations have been developed for decades. For example, the fast multilevel preconditioned iterative scheme, the overlapping Schwarz method and so on. Most of the existing methods are designed for solving the original indefinite problem directly. The paper by L. Q. Zhong et al. [J. Comput. Math. 27, No. 5, 563–572 (2009; Zbl 1212.65467)] presents two types of iterative two-grid methods for the edge finite element approximation of the time-harmonic Maxwell equations. One is to add the kernel of the \(\operatorname{curl}\)-operator in the finite space to a coarse mesh space to solve the original problem. The other is to use an inner iterative method for dealing with the kernel of the \(\operatorname{curl}\)-operator in the fine space and the coarse space, separately. Comparing with the other existing solvers for time-harmonic Maxwell equations, the two-grid methods mainly amount to the solution of an \(H(\operatorname{curl})\)-elliptic problem in a fine mesh space, which has many high-efficiency fast solvers. Moreover, the work in a coarse space is relatively negligible. Numerical experiments in this paper support the efficiency of the methods. Therefore I think the authors of this paper have developed a very effective way for solving the time-harmonic Maxwell equations by the edge element.