Being considered are the selection problems of rational thermodynamic parameters and control laws for hydrogen and hydrogen-oxigen aero-turbo-rocket (ATR) engines designed for horizontal take-off and landing Single-Stage-to-Orbit (SSTO) vehicles acceleration up to Mach 6. Three types of ATR-engines were studied: gas generator, expander, gas generator with H2 preheating. Computation allows for thermodynamic features of cryogenic - fuelled engines, operating within a wide flight speed envelope. Construction materials performance corresponded to world practice 2005-2010 years forecast. Relative payload mass was used for estimations of different type ATR-engines effectiveness for SSTO.