High vehicle fuel efficiency is achieved by reducing fuel consumption during driving both in the city and on the highway. During driving in the city, the system accumulates the energy derived from vehicle motion during braking, and uses it to assist in vehicle propulsion at a later time. The energy can be stored either in a compressed-air reservoir or in an electric battery. During cruising on the highway, the engine operates in a two-stage gas-expansion cycle. The engine has primary and secondary cylinders. Only primary cylinders operate in internal-combustion mode. After expansion in primary cylinders, combustion gas is subjected to a second stage of expansion in secondary cylinders. This substantially improves the engine efficiency. Whenever heavy engine load is needed, all cylinders operate in internal-combustion mode.