This work relates the theoretical study of the dynamic behavior of a dual free-piston Stirling engine (DFPSE) coupled with an asynchronous linear alternator. This machine integrates one piston and two displacers placed in a symmetrical way compared to the piston to improve the stability of the machine. The paper presents an analytical study of the dynamic balance equations of a DFPSE. This model takes into account the non-linear dissipative effects of the fluid and the electromagnetic forces. The dynamic balance equations of the machine are solved by means of linearized pressure in the time domain especially. The objective is to evaluate the thermo-mechanical conditions for stable operation of the engine. The developed model may be used to simulate the dynamic behaviour of a built engine. The DFPSE produces a mechanical power of 1 kW and it has a design operating point of 1.4 MPa corresponding to the frequency about 22 Hz. Helium is the working fluid. This machine is designed to be used as a micro combined heat and power (μCHP) system for combined generation of electricity and heat.