A mathematical model of the working processes in positive-displacement machines designed to compress two-phase, two-component working fluids is developed on the basis of the general laws of conservation of energy, mass, volume and motion. A mathematical model of the working processes of a hybrid piston power machine where there is a layer of liquid above the piston in the compressor section is given. Two open thermodynamic systems (gas and droplet liquid) in the presence of deformation and thermal interactions are considered.