The functioning of a modern economy cannot be studied on the basis of models of the neoclassical school. They are not provided for such phenomena as asymmetry and incomplete information. They do not take into account possible risks when making decisions, and do not find a place for such effects of information asymmetry as an unwanted selection, moral hazard and opportunistic behaviour of the parties. Based on its review of the results of practical research problems of adverse selection and moral hazard in the various markets of insurance services the authors analyze the ways to combat these phenomena and offer their own solutions for the specific situations. Study of the problems of adverse selection on the insurance market is one of the stages of many years of the original research in the framework of the contracts theory