The purpose of this article is to give a general idea of the theory of choice sequences (TCS) which is of great importance in the intuitionistic mathematics, and to correct some common misunderstanding on the law of the excluded middle. In § 1 the fundamental concepts of TCS are discussed informally. In §§ 2 and 3 it is shown that some laws, which are established in the classical system, can be refuted in TCS. In § 4 a formulation of some Kripke-model in TCS is given on the basis of the suggestions made by Kripke.