Purpose. The development of the free-piston diesel engine-and-hydraulic pump for the continuously variable hydrostatical transmission of mobile power vehicles. Methodology. For a long time engine builders have been interesting in the problem of developing free piston engines, which have much bigger coefficient of efficiency (40…80%). Such engines don’t have the conversion of reciprocating motion for inner combustion engine piston into rotating motion of crankshaft, from which the engine torque is transferred to the power machine transmission. Free-piston engines of inner combustion don’t have the crank mechanism (CM) that significantly reduces mechanical losses for friction. Such engines can be used as compressors. Free-piston engine compressor (FPEC) – is a free-piston machine in which energy received from engine’s cylinder is being transferred direct to compressor’s pistons connected with operational pistons of engine without crank mechanism. Part of the pressed air is being consumed for engine cylinder drain and the other part is going to the consumer. Findings. The use of free-piston engines-and-hydraulic pumps as power-transmission plants of power vehicles (diesel locomotives, combine harvester, tractors, cars and other mobile and stationary power installations) with the continuously variable transmissions allows cost effectiveness improvement and metal consumption reduction of these vehicles, since the cost effectiveness of FPE is higher by 25-30%, and the metal consumption is lower by 40-50%. Originality. One of the important advantages of the free-piston engines is their simplicity and engine balance. As a result of the crank mechanism absence their construction is much simplified and the vibrations, peculiar to the ordinary engines are eliminated. In such installation the engine pistons are directly connected through the rod to compressor pistons and therefore there are no losses in the bearing bushes. Practical value. The free-piston engines are now used only as gas generators and diesel compressors, and the hydraulic transmission is arranged with the ordinary heat-engine, which operates the hydraulic pumps.