Experimental researches on establishment of technical parameters of intermediate rail fastenings concerning maintenance of longitudinal stability of rail threads, establishment of technical parameters of intermediate rail fastenings on maintenance of longitudinal stability of rail threads are carried out. The researches of influence of technical characteristics of hardness at interaction of a rail and a wheel and their influence on the level of longitudinal forces of interaction between elements of a track and wheels of a rolling stock in operation on the railways of Ukraine are analyzed. After the start of operation of wheel pairs with the increased value of hardness the optimum ratio of hardness of rail and wheel steel was broken. It is known from various sources regarding the interaction of the rail and the wheel that metals with approximately same hardness show better wear resistance in the friction pair. Based on the obtained data, calculations were performed and their analysis was carried out with the development of recommendations for further operation.