A method for the synthesis of new 1-aminoadamantane derivatives, the N-adamantylamides of arylsulfonyl(sulfanyl)propionic acids, is developed. It was shown that the reaction of arylsulfonyl(sulfanyl)propionitriles with 1-hydroxyadamantane under the classical conditions of the Ritter reaction (in a mixture of acetic and concentrated sulfuric acids) made it possible to obtain the desired products with a 58-75% yield. Direct experimental confirmation of the mechanism of this reaction was obtained via isolation of its intermediate in the pure state.