Maxwells equations provide the foundation for the theory of electromagnetism,and solving these equations numerically is an important task in many applications.For problems posed on a cuboid or on R3,the alternating direction implicit method proposed by Zheng,Chen,and Zhang (2000) is particularly attractive,because this method is unconditionally stable and computationally cheap.The main idea is,roughly speaking,to decompose the Maxwell operator in such a way that the sub-flows can be propagated in a stable and efficient way. In this talk,second-order convergence for the semi-discretization in time is shown in the framework of operator semigroup theory.The proof is based on results concerning the regularity of the Cauchy problems of the subflows,which then allow to apply an abstract convergence proof by Hansen and Ostermann (2008). Before the error analysis,well-posedness of Maxwells equations on cuboids and on R3 will be discussed.