Abstract New types of electric machines with the rotors containing bulk HTS (YBCO and Bi–Ag) elements are presented. Different schematics of hysteresis, reluctance, “trapped field” and composed synchronous HTS machines are discussed. The two-dimensional mathematical models describing the processes in such types of HTS machines were developed on the basis of the theoretical analysis of the electrodynamic and hysteresis processes in the single-domain and polycrystal YBCO ceramic samples and plate shape Bi–Ag elements. The test results of the series of hysteresis, reluctance, “trapped field” and composed with permanent magnets HTS motors with output power rating 0.1–18 kW and current frequency 50 and 400 Hz are given. These results show that in the media of liquid nitrogen the specific output power per one weight unit of HTS motors is 4–7 times better than for conventional electric machines. Comparison of the theoretical and experimental characteristics of the developed HTS motors show that they are in good agreement. The test results for liquid nitrogen cryogenic pump system with hysteresis 500 W HTS motor are discussed. The designs and first test results of HTS motor operating in the media of liquid nitrogen with output power 100 kW and power factor more than 0.8 are given. Future development and applications of new types of HTS motors for aerospace technology, on-land industry and transport systems are discussed.