Disclosed embodiments of proposed hydrogen-oxygen and hydrogen-air engines are usable in automotive, power-producing, and other industries. The engines comprise cylinders; water dissociation units, including thermo-impact transformers and possibly electrolyzers; ionic dividers separating hydrogen and oxygen ions; injection chambers configured to inject hydrogen and oxygen/air doses in response to an operator's action and according to proposed dosing methods accounting a hydrogen-oxygen optimal ratio suitable for an explosive plasma reaction in the cylinders, increasing engines torque, eliminating/reducing pollutions. Determination of optimal ratios for hydrogen-air mixtures is also discussed. The dosing methods include algorithms for computing termination injection pressures for hydrogen-oxygen /air doses. Different hydrogen-oxygen/air delivery system are described in conjunction with modified dosing methods. The delivery systems are exemplarily connected to hydrogen and oxygen tanks, or to a hydrogen tank and a compressed-air container variously communicating with the ionic dividers.