NOVELTY - The method involves controlling the operation of engine (10) and vehicle in response to driver's demands. Two cylinders (12,72) of engine are alternately connected to outside atmosphere and to gas transfer unit. The engine is operated in two-stage gas expansion mode in which useful mechanical work is performed on pistons (14,74) provided in the cylinders using only internal energy still remained in pressurized combustion gas after its expulsion from main cylinder (12), for responding to demand of vehicle-propulsion force, so that additional useful energy is extracted from combustion gas.    USE - Method for operating vehicle such as heavy truck, bus, etc., in city and on highway.    ADVANTAGE - High vehicle-fuel efficiency during cruising with appropriate constant speed on highway and during stop-and-go driving in city, can be improved at low cost with simple procedures, by reducing fuel consumption of vehicle, as the engine is operated in two-stage gas expansion mode in which useful mechanical work is performed on a piston provided in the cylinders using only internal energy still remained in pressurized combustion gas after its expulsion from main cylinder, for responding to demand of vehicle-propulsion force, so that additional useful energy is extracted from combustion gas, without using additional fuel energy, and without the need of providing large-sized compressed air-reservoir, while reducing harmful exhaust emissions, and improving engine efficiency. Temporary storage of energy dissipated during vehicle deceleration and effective utilization of temporarily stored energy during vehicle acceleration can be easily achieved, and hence fuel consumption at the time braking and acceleration of vehicle can be reduced. The need of electric started in the air-hybrid system can be avoided as the engine is started with compressed air received from air reservoir. The need of exhaust gas recirculation system can be avoided, as sufficient amount of residual gas is trapped in each cylinder at the end of each exhaust stroke to control the amount of nitrogen oxide produced in the next cycle without the need of exhaust gas recirculation.    DESCRIPTION OF DRAWING(S) - The drawing shows the schematic cross-sectional side view of the engine cylinder and their gas-flow connection to outside atmosphere, and compressed air-reservoir.    Engine (10)    Cylinders (12,72)    Pistons (14,74)    Cylinder chambers (20,80)    Compressed air reservoir (46)